GIMC SIMAI Young 2026

3 Jun 2026, 09:00 → 5 Jun 2026, 18:00 Europe/Rome

Pisa

Cecilia Pagliantini (University of Pisa), Giovanni Stabile (Sant'Anna School of advanced studies), Paolo Sebastiano Valvo, Milo Viviani

Overview

The Gruppo Italiano di Meccanica Computazionale (GIMC) and the Società Italiana di Matematica Applicata e Industriale (SIMAI) are delighted to announce the third edition of their joint workshop for young scientists (aged ≤ 35), set to take place in Pisa on June 3-5, 2026.

Scope

The workshop aims at providing participants with a platform to exchange their most recent results, stay current on new trends, and foster meaningful interactions. The program includes plenary lectures by leading scientists, a dedicated session for recipients of the GIMC and SIMAI Young Researchers Awards, parallel thematic sessions organized by participants. In the case of an excessive number of oral presentations, some contributions may be accepted for a poster session. Contributions from all areas of applied mathematics and computational mechanics are warmly welcomed, in the form of an oral presentation or a poster to be showcased during a dedicated poster session.

Organizers

Workshop chairs: Cecilia Pagliantini (University of Pisa), Giovanni Stabile (Sant'Anna School of Advanced Studies), Paolo S. Valvo (University of Pisa) e Milo Viviani (Scuola Normale Superiore).

GIMC Advisory board: Giovanni Garcea (President, University of Calabria), Francesco Marmo (University of Naples “Federico II”), Michele Marino (University of Rome “Tor Vergata”).

SIMAI Advisory board: Gianluigi Rozza (President, International School for Advanced Studies, Trieste), Stefania Bellavia (University of Florence), Dajana Conte (University of Salerno), Marco Verani (Polytechnic University of Milan).

Organising committee members: Gennaro Calandriello (Sant’Anna School of Advanced Studies), Paolo Fisicaro (University of Pisa), Lucia Lottici (University of Pisa), Nemo Malhomme (Sant’Anna School of Advanced Studies), Mario Milazzo (University of Pisa), Niccolò Picchiarelli (Sant’Anna School of Advanced Studies), Marco Picchi Scardaoni (University of Pisa), Pietro Tavazzi (Sant’Anna School of Advanced Studies).

Acknowledgements

This event has been organized with the financial support the Associazione Italiana di Meccanica Teorica e Applicata (AIMETA), the Istituto Nazionale di Alta Matematica "Francesco Severi" - Gruppo Nazionale di Calcolo Scientifico (INDAM - GNCS), and the European Research Council (ERC) - StG DANTE GA 101115741 (PI Giovanni Stabile), and under the patronage of the Department of Civil and Industrial Engineering (DICI) of the University of Pisa and the Società Italiana di Scienza delle Costruzioni (SISCo).

Download GSY26-Poster.pdf

Wednesday 3 June

09:30 → 12:30 Registration

14:10 → 14:30 Opening of the workshop

14:30 → 15:15 Plenary talk: Mixed dimensional problems on non-matching grids at the exascale: solutions, challenges, and perspectives

This presentation addresses the challenges and solutions associated with mixed-dimensional problems on non-matching grids, with a perspective towards exascale computing. Many physical phenomena involve coupled partial differential equations (PDEs) defined on domains of heterogeneous dimensions, leading to non-matching coupling at the interfaces. To tackle these problems, the reduced Lagrange multiplier method [2] provides a general mathematical framework for analysis and approximation. This approach sheds light on the stability, well-posedness, and error associated with dimensionality reduction, but requires the efficient solution of saddle point problems involving non-matching discretizations.
For the efficient numerical solution of the resulting large-scale systems, particularly on complex geometries like vascular networks embedded in biological tissues [1], we borrow a technique that was developed for non-nested multigrid methods, which offer the required flexibility by allowing the exchange of information between arbitrarily overlapping and distributed grid hierarchies with a matrix-free implementation [3], and we developed augmented Lagrangian-based preconditioners that offer optimal and scalable solutions [4].
The continued development of such robust and scalable algorithms within high-performance finite element libraries like deal.II is crucial for tackling these challenging problems at the exascale.

[1] Luca Heltai, Alfonso Caiazzo, and Lucas O. Müller, Multiscale coupling of one-dimensional vascular models and elastic tissues, Annals of Biomedical Engineering 49 (2021), 3243–3254.

[2] Luca Heltai and Paolo Zunino, Reduced lagrange multiplier approach for non-matching coupling of mixed-dimensional domains, Mathematical Models and Methods in Applied Sciences 33 (2023), no. 12, 2425–2462.

[3] Marco Feder, Luca Heltai, Martin Kronbichler, and Peter Munch, Matrix-free implementation of the non-nested multigrid method, Arxiv, 2024.

[4] Michele Benzi, Marco Feder, Luca Heltai, and Federica Mugnaioni, Optimal and scalable augmented Lagrangian preconditioners for fictitious domain problems, Arxiv, 2025.

Speaker: Luca Heltai (Università di Pisa)

15:15 → 15:45 Junior plenary talk: Enhancing Spatial Filters for Convection-Dominated Flows: VMS Models and Parameter Optimization

The evolve-filter (EF) strategy is a spatial filter-based numerical stabilization technique for convection-dominated flows. In under-resolved regimes, classical numerical approaches may lack accuracy due to the presence of spurious numerical oscillations. EF offers a simple, modular, and effective approach to smooth out these instabilities.
However, it is well known that when the filter action is too strong, the method may lead to inaccurate and over-diffusive results.

In this talk, we present novel strategies to mitigate the over-diffusivity of EF when large filter radii are employed, while preserving the main flow features. We explore two complementary directions: modifying the model and optimizing its parameters.

From an algorithmic perspective, we propose a new approach based on the variational multiscale (VMS) framework, which allows us to separate the resolved large scales from the resolved small scales in the evolved velocity field. The filtered small scales are then used to correct the large scales, enhancing accuracy without losing important flow information.

From an optimization perspective, we demonstrate the crucial role of the filter parameter and introduce a reinforcement learning strategy for its selection. Notably, the training of the network does not rely on direct numerical simulations, significantly reducing the computational cost of the learning procedure.

Speaker: Maria Strazzullo (Politecnico di Torino, DISMA)

15:45 → 16:15 Coffee break

16:15 → 18:00 MS04.1 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

16:15 Adapted W Methods for Efficient and Accurate Solution of Parabolic PDEs

Parabolic PDEs are widely used to model phenomena evolving in time and space, but their numerical solution requires efficient time integration combined with suitable spatial discretizations.
Thus, we investigate approaches to improve the efficiency of pre-existing methods used as time integrators for the ODE system arising from the spatial semi-discretization of the given PDE. Considering W methods of order up to four [1,4,5] as underlying schemes, we compare the use of AMF (Approximate Matrix Factorization) and matrix-oriented techniques. We show that, by exploiting the structure of the matrices arising from the spatial discretization of the diffusion operator, these approaches significantly reduce computational cost, while preserving the desired stability and accuracy properties [2].
Second, we investigate the improvement of the accuracy of the AMF-W methods when PDEs with time-dependent boundary conditions are considered. In such cases, AMF schemes may suffer from order reduction. Thus, we will exploit the application of boundary correction techniques that aim to recover the expected order of accuracy, exploiting problems with several typologies of boundary conditions in multiple space dimensions [3,4].

References

1. D. Conte, S. González-Pinto, D. Hernández-Abreu, and G. Pagano. On approximate matrix factorization and TASE W-methods for the time integration of parabolic partial differential equations. J. Sci. Comput. 100(2), 34. 2024.
2. D. Conte, S. Iscaro, G. Pagano. On Matrix-Oriented and AMF-W Methods for advection-reaction-diffusion Partial Differential Equations. In preparation.
3. S. González-Pinto, D. Hernández-Abreu, S. Iscaro. On the treatment of boundary conditions for AMF-W methods in diffusion-reaction PDEs. In preparation.
4. González-Pinto, S., Hernández-Abreu, D. Boundary corrections for splitting methods in the time integration of multidimensional parabolic problems. Appl. Numer. Math., 210: 95-112. 2025.
5. W. Hundsdorfer, J. G. Verwer. Numerical solution of time-dependent advection diffusion-reaction equations. Vol. 33. Springer Science and Business Media., 2003.

Speaker: Samira Iscaro (Department of Mathematics, University of Salerno)

16:30 A numerical-experimental comparison of Dog-Bone ductile sample via high-order isogeometric phase-field model for brittle fracture

The study of fracture mechanics is one of the most contemporary topics in engineering. Accurate prediction of the fracture phenomenon enables improvements in the design of structural elements, significantly impacting society through economic savings. Preventing fractures reduces repair costs, material loss, pollution from spills of environmentally impactful substances, and loss of life.

The development of computational technologies has directed the attention towards numerical models for the study of fracture. Among these, the phase-field model has gained prominence [1]. This mathematical model allows to capture interface phenomena by approximating a discontinuous interface in a continuous manner. Recently, it has been shown that this approximation can be achieved by employing high-order functionals in order to reduce the computational cost [2], discretizing the high-order operator by means of Isogeometric Analysis (IGA) [3].

In this contribution, the high-order AT2 phase-field model [4] is employed to investigate the numerical–experimental comparison for a case study involving an EN AW-6060 aluminum specimen, with the aim of qualitatively reproducing the experimental results through the crack pattern evolution and quantitatively capturing the maximum developed load.

[1] B. Bourdin, G. Francfort, and J.-J. Marigo, “Numerical experiments in revisited brittle fracture,”Journal of the Mechanics and Physics of Solids, vol. 48, no. 4, pp. 797-826, 2000.
[2] L. Greco, E. Maggiorelli, M. Negri, A. Patton, and A. Reali, “AT1 fourth-order isogeometric phase-field modeling of brittle fracture,” Mathematical Models and Methods in Applied Sciences, vol. 35, no. 13, pp. 2741-2795, 2025.
[3] T. Hughes, J. Cottrell, and Y. Bazilevs, “Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement,” Computer Methods in Applied Mechanics and Engineering, vol. 194,no. 39, pp. 4135-4195, 2005.
[4] L. Greco, A. Patton, M. Negri, A. Marengo, U. Perego, and A. Reali, “Higher order phase-field modeling of brittle fracture via isogeometric analysis,” Engineering with Computers, pp. 1-20, 2024.

Speaker: Luigi Greco (University of Pavia)

16:45 A stochastic perturbation approach to nonlinear bifurcating problems via Polynomial Chaos Expansion

Incorporating probabilistic terms into mathematical models is essential for Uncertainty Quantification in complex systems. However, standard stochastic methods, such as Monte Carlo simulations, are often computationally intensive, particularly when investigating ill-conditioned problems such as bifurcating phenomena in parameter-dependent PDEs, which require running a large number of simulations across different parameter values. In contrast, this work presents a Spectral Stochastic Finite Element Method (SSFEM) framework, based on generalized Polynomial Chaos Expansion (PCE), that captures system properties while requiring only a few runs of the nonlinear solver for the resulting Galerkin system.

The proposed approach analyzes a perturbed version of the original problem, employing PC coefficients to reconstruct bifurcation diagrams without the need for extensive parameter sampling. The methodology is grounded in the theoretical analysis of one-dimensional normal forms in dynamical systems, where we characterize two distinct solution families: oscillating solutions, which emerge when multiple stable states coexist, and branch-approximating solutions, which track specific bifurcation branches. Together, these provide both analytical convergence results and statistical properties that enable the identification of bifurcation branch locations.

We extend this surrogate methodology to high-dimensional PDEs, specifically applied to problems in continuum mechanics. The results demonstrate that PC coefficients yield significant statistical information regarding the solution manifold, offering a scalable path for the high-order numerical analysis of complex phenomena.

Speaker: Giacomo Venier (SISSA)

17:00 Operator Splitting Scheme for Nonlocal Kinetic PDEs derived from Multi Agent Systems

Kinetic models obtained as the mean field limit of interacting particle systems provide an effective framework for describing collective dynamics in a wide range of applications, including vehicular traffic modeling, coordinated animal motion, biological population dynamics, and the control of robotic swarms. Compared to direct multi agent simulations, the continuous formulation based on Fokker–Planck type equations drastically reduces the computational cost as the number of agents increases, while preserving an accurate description of the macroscopic behavior.
In this work, we present a numerical method for the simulation of a class of nonlocal kinetic equations with nonlinear drift, derived from an underlying particle interaction model. The strategy relies on an operator splitting approach that separates the transport term from the drift–diffusion dynamics. Transport is discretized using an explicit Lax–Wendroff scheme, while the velocity drift–diffusion part is treated with a Chang–Cooper method, ensuring stability, mass conservation, and positivity of the solution. The combination of these two components yields a robust and accurate scheme.
The method is validated by comparing the PDE solution with that of the original particle model, showing excellent agreement between the two descriptions and confirming the correctness of the mean field limit. We also analyze the computational cost of both approaches, highlighting how the kinetic formulation becomes significantly more efficient beyond a certain threshold in the number of agents.
These results demonstrate that the kinetic formulation, combined with accurate numerical schemes, provides an effective tool for the simulation of complex systems driven by collective interactions.

Speaker: Simone Accogli (Università di Pavia)

17:15 A variational finite element approach for stiff non-convex Cahn–Hilliard systems in structural topology optimization

Higher-order partial differential equations play an increasingly important role in structural topology optimization, particularly in level-set, phase-field, and thermodynamically consistent variational formulations arising in advanced applications such as lightweight structural design, multifunctional materials, compliant devices, and additive manufacturing.
In this work, we consider a topology optimization setting coupling a static mechanical model, taken here as linear elasticity for simplicity, with a fourth-order Cahn–Hilliard-type phase-field equation. The resulting problem is strongly nonlinear, nonconvex, and stiff, thus posing significant challenges for robust numerical solution. To address these difficulties, we adopt a variational formulation in which the coupled system is recast as a constrained optimization problem. Time discretization is performed by a fully implicit Euler scheme, while the spatial approximation relies on a mixed finite element formulation with standard finite elements, introducing an auxiliary field to reduce the original fourth-order phase-field equation to a system of two second-order equations. Pointwise constraints are enforced through a simple bound-enforcement strategy, which in turn influences the nonlinearity, convexity, and conditioning of the discrete problem. To further improve robustness, we employ a continuation technique acting on the phase-field free energy. The resulting framework provides a practical and flexible route for the numerical treatment of higher-order PDE-constrained topology optimization problems.

Speaker: Edmund Bell-Navas (Universidad Politécnica de Madrid)

16:15 → 18:00 MS05 - Multiscale Cardiac Electrophysiology: From Scalable Computational Solvers to Patient-Specific Simulations

16:15 A Computational Model of Human iPSC-Derived Ventricular Myocyte for Calcium-Mediated Arrhythmia and Disease Modeling

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are widely used to investigate inherited and acquired cardiac disorders in a patient-specific context. However, their immature electrophysiological phenotype requires quantitatively calibrated dynamical models capable of mechanistically describing nonlinear calcium–voltage coupling across multiple temporal scales.

We develop a ventricular hiPSC-CM ionic model formulated as a stiff system of 28 coupled nonlinear first-order ordinary differential equations. Building upon the Paci2020 framework, we replace the original Hodgkin–Huxley description of the L-type calcium current (ICaL) with a finite-state Markovian scheme. This formulation separates voltage-dependent and calcium-dependent inactivation into two interconnected four-state loops, with channel transitions governed by voltage- and calcium-dependent rates that ensure probability conservation.

Mathematically, the resulting system defines a high-dimensional nonlinear dynamical flow characterized by tight coupling among membrane voltage, gating variables, and intracellular calcium compartments. Such ionic models display marked sensitivity to parameter variations and initial conditions: small perturbations in conductances or transition rates may produce substantial changes in action potential morphology, repolarization dynamics, or oscillatory behavior, reflecting the complex stability structure of the nonlinear system.

Parameter identification is performed through automatic optimization in two stages. First, the Markovian ICaL submodel is calibrated by minimizing a weighted least-squares objective via the Nelder–Mead simplex algorithm. Second, global optimization is carried out against experimental biomarkers of spontaneous action potentials and calcium transients obtained from in vitro patch-clamp recordings.

Pharmacological and genetic perturbations are modeled as structured modifications of transition rates within the Markov framework, enabling consistent interpretation within the same nonlinear system. The resulting model provides a robust and quantitatively identified platform for studying calcium-mediated arrhythmogenesis and supports scalable multiscale cardiac electrophysiology investigations.

References
[1] Francesca Simone, et al. A novel computational model of human iPSC-derived ventricular myocytes with improved [l]-type calcium current for application to Timothy syndrome. Scientific Reports, February 2026.

Speaker: Francesca Simone (Università degli Studi di Pavia)

16:30 Coupling cardiac electrophysiology models: from fine-scale to coarse-scale simulations

The well-established homogenized bidomain (BD) model represents averaged intra- and extracellular behavior, providing a good compromise between physiological accuracy and computational feasibility. However, as the myocyte is not present in the model, the BD model cannot account for cell-to-cell variations, which can be properly analyzed by adopting the cell-based EMI model, in which the extracellular (E) space, the cell membrane (M) and the intracellular space (I) are explicitly represented. However, its prohibitive computational cost restricts its application to small domains.
Finally, the recent Kirchhoff Network model (KNM) models each cell and its surrounding extracellular space as computational nodes. Although it cannot reach the subcellular resolution of the EMI model, it preserves essential conduction properties and has computational demands that are comparable to the bidomain model.

These observations highlight a general challenge in cardiac modeling: homogenized models are often inadequate for investigating pathological conditions, while highly detailed models are unnecessarily expensive in simulations where the majority of the myocardium is healthy. This scenario motivates a multiscale modeling strategy: reduce the overall computational cost by adopting fine-scale models in the diseased regions and coarser models in the surrounding healthy tissue, where efficiency is prioritized over accuracy.

To leverage the strengths of these complementary models, we employ a domain decomposition approach, in which each subdomain can be solved independently and the solutions are coupled through interface conditions. In the case of non-overlapping regions, we have to impose the continuity of both the solution and the flux, while in the case of overlapping subdomains, continuity of flux comes naturally from enforcing the solution is consistent pointwise in the overlapping region. This domain decomposition strategy not only facilitates parallel computation and handling of complex geometries but also provides flexibility to use different solvers in subdomains.

Speaker: Sara Demo

16:45 Second Order IMEX Time Stepping Methods for Efficient Multi-Electrode Array simulations

Multi-electrode arrays (MEAs) enable tissue-level electrophysiological studies of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) by recording extracellular field potentials (FPs). Recent in-silico models have improved MEA simulations by coupling detailed electrode descriptions with the Bidomain framework, a parabolic-elliptic system of nonlinear PDEs coupled with a stiff ionic model.
The standard numerical strategy relies on operator splitting techniques that decouple the PDE and ODE components. In most existing implementations, the ionic subsystem is treated explicitly while the diffusive Bidomain operator is handled implicitly, leading to first-order Implicit-Explicit (IMEX) time discretizations. Although computationally convenient, this approach limits temporal accuracy and may compromise efficiency in large-scale simulations.
In this work, we revisit this framework and investigate higher-order IMEX Runge–Kutta schemes within the Strang operator splitting, specifically tailored for the Bidomain–MEA setting. The proposed method preserves the computational advantages of the IMEX structure while achieving higher temporal accuracy without increasing algorithmic complexity. We compare first- and second-order schemes in terms of computational cost and global error with respect to a high-fidelity reference solution computed with a very small time step. For a fixed computational time, the higher-order scheme significantly enhances accuracy. These results demonstrate that increasing the temporal order within an IMEX operator-splitting framework provides tangible efficiency gains and enhances the reliability of large-scale MEA simulations.

Speaker: Sofia Tonali (Università di Pavia)

17:00 Neural Network Emulators for Cardiac Electrophysiology Modeling in Derived Stem Cardiomyocytes

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC--CMs) provide a physiologically relevant platform for studying cardiac electrophysiology under both healthy and pathological conditions, as well as for drug cardiotoxicity screening. Multi-electrode arrays (MEAs) enable non-invasive, long-term recording of extracellular field potentials from hiPSC-CM monolayers, capturing cellular electrical activity across pharmacological perturbations and disease phenotypes.

Existing ionic models for hiPSC-CMs — for both ventricular--like and atrial--like phenotypes— replicate action potential morphology by simulating voltage-dependent ion channel kinetics and intracellular calcium handling. While these models capture the underlying biophysics, their computational cost becomes prohibitive when exploring large parameter spaces, performing uncertainty quantification, or solving inverse problems to estimate conductances from experimental data. Approaches through population of models, which generate heterogeneous virtual cohorts by sampling conductance parameters, further exacerbate this computational burden.

We present a deep learning framework that leverages neural network emulators to approximate hiPSC-CM ionic models with several orders of magnitude speedup while maintaining sub-millisecond accuracy. Trained on synthetic populations, the emulator enables real-time forward simulation across physiological variability.

This methodology bridges high-throughput experimental electrophysiology with mechanistic modeling, providing a scalable tool for drug safety assessment, disease phenotyping, and precision cardiology. By reducing simulation time, our approach unlocks previously intractable applications in parameter estimation, sensitivity analysis, and virtual clinical trials.

Speaker: Sofia Botti (MOX, Politecnico di Milano)

17:15 Multimodal Personalisation of Cardiac Electrophysiology Models Integrating 12-Lead ECG and CT Imaging

Recent advances in cardiac electrophysiological modelling, coupled with modern computational technology, enable fast in silico simulation of ventricular tachycardia (VT), showing strong potential for applications in arrhythmia risk stratification and therapy planning, such as catheter ablation. However, accurate patient-specific model personalisation remains a major challenge, limiting simulation fidelity and hindering clinical translation. In this work, we develop a multimodal personalisation framework that combines cardiac structural information derived from computed tomography (CT) with electrical characteristics extracted from 12-lead electrocardiograms (ECGs).

We studied six patients undergoing electrophysiological studies. Sinus rhythm 12-lead ECG signals were extracted from EP recordings and used as the objective for parameter optimisation. Pre-ablation CT scans were used to construct patient-specific biventricular simulation domains and to estimate ECG lead positions. Building on prior work in which in silico VT induction was achieved using EP models personalised from CT-derived myocardial wall thickness (WT), we implemented a two-stage optimisation framework consisting of early activation onset estimation followed by optimisation of EP model parameters. Following early-onset estimation, the simulated 12-lead ECG signals achieved an average QRS peak accuracy of 91.20%. With optimised parameters, the average QRS duration error was reduced to 3.94 ms, compared with 37.42 ms using baseline parameters. The complete in silico VT induction pipeline was subsequently applied to patients with adequate electroanatomical VT mapping data (n = 4). Using the personalised parameters, clinically observed VT patterns were successfully reproduced, with VT cycle lengths closer to the recorded values than those obtained with baseline parameterisation. More importantly, in-silico VT induction succeeded in one patient for whom it had previously failed when using baseline parameters.

Speaker: Buntheng LY (Institut Hospitalo-Universitaire Liryc, France)

16:15 → 18:00 MS06.1 - Numerical Modeling for Sustainability Problems

16:15 Discovering physical laws through Neural ODEs

We present a novel hybrid computational framework designed to reconstruct the hidden dynamics of critical parameters in complex dynamical systems [1]. In many scientific applications, the predictive accuracy of physics-based models is often limited by the inaccurate extrapolation of time-varying parameters. To address this problem, we propose an hybrid framework that integrates Neural Ordinary Differential Equations (Neural ODEs) within a classical differential solver to learn the underlying evolution laws governing these parameters.

The architecture consists of a data-driven layer that models parameter trajectories as a function of exogenous signals and sample-specific latent variables. These learned parameters are then seamlessly integrated into a physics-based. To handle data heterogeneity and noise, we incorporate a data assimilation procedure that estimates latent input variables through an end-to-end optimization process.

From a numerical perspective, this approach leverages the flexibility of deep learning while maintaining the mathematical consistency of physical models. We validate the framework within the context of computational epidemiology, proving robustness with respect to noise and long-term stability compared to traditional emulators. Numerical results entail that this hybrid strategy is effective for discovering parameter laws and it is especially reliable for long-term forecasting in noisy, real-world scenarios.

[1] Ziarelli, G., Pagani, S., Parolini, N., Regazzoni, F., & Verani, M. (2025). A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts. Computer Methods in Applied Mechanics and Engineering, 437, 117796.

Speaker: Giovanni Ziarelli (MOX Laboratory, Department of Mathematics, Politecnico di Milano)

16:30 Stochastic First-Order Methods for Large-Scale Regularized Inverse Problems

A wide range of applications in imaging, data science, and machine learning can be formulated as discrete inverse problems of the form
\begin{equation}
y = Kx + \varepsilon,
\end{equation}
where $K$ is a linear operator, $x \in \mathbb{R}^d$ is the unknown variable, and $y$ represents noisy observations.
Due to ill-conditioning and the increasingly large scale of modern problems, direct inversion is unstable or computationally infeasible.
A common approach is to adopt a variational formulation, in which the solution is obtained by minimizing a functional composed of a data fidelity term and a regularization term.

Deterministic first-order optimization methods are classical tools for solving such problems, but their computational cost can be prohibitive when the number of measurements is very large.
Stochastic optimization methods offer an effective alternative by reducing the cost per iteration through randomized sampling strategies.
These methods exploit the structure of the problem by operating on subsets of the data, while still ensuring convergence under appropriate assumptions.

In this work, we investigate stochastic first-order methods for regularized inverse problems, focusing on adaptive strategies for step-size selection and variance control.
We analyze the role of mini-batch sampling and dynamically tuned hyperparameters in improving convergence speed and robustness.
The proposed approach builds upon recent advances in stochastic gradient methods with adaptive learning rates and variance reduction, extending their use beyond traditional machine learning applications.

Numerical experiments on representative large-scale problems demonstrate the effectiveness and scalability of the proposed stochastic framework.

Speaker: Ilaria Trombini (University of Ferrara)

16:45 A physics-Informed Covariance Kernel on Networks for the Uncertainty Quantification of Sea Surface Temperature

We present a physics-informed geostatistical framework for modeling Sea-Surface Temperature (SST) variability, bridging the gap between deterministic numerical models and stochastic uncertainty quantification. While numerical models like ERSEM provide valuable point predictions, they often lack the probabilistic framework necessary for comprehensive risk assessment of rising water temperatures. We model the residuals of the point projections, leveraging an overlapping period of the model’s estimation and real satellite data observations.
We aim to characterize the covariance structure of the residuals, in order to embed future water temperature into a Gaussian Random Field (GRF), with mean given by the ERSEM projections and covariance operator estimated from the empirical residuals.
Traditional Euclidean modeling often fails in marine environments because it ignores complex domain geometries and the inherent anisotropy of water currents. We address this by discretizing the domain into a directed network that explicitly excludes landmasses. Within this network, we define a Markov chain where transition probabilities are derived from current velocity fields. We then construct a valid, positive definite covariance structure that respects this network topology and the advective transport induced by currents.
This approach allows for rigorous Monte Carlo simulations that remain physically grounded while ensuring mathematical consistency. The resulting framework enhances risk assessment capabilities—including early hot-spot detection and joint exceedance probability estimation—by providing full distributional forecasts. Incorporating physical flow constraints into the covariance operator yields a parsimonious yet powerful tool for characterizing uncertainty in complex marine environments.

Speaker: Leonardo Marchesin (MOX - Department of Mathematics, Politecnico di Milano)

17:00 Identifying Stochastic Sparse Models with SINDy algorithm

Sparse regression techniques enable the extraction of governing equations directly from measurement data, allowing efficient identification of nonlinear system dynamics with minimal complexity. This work presents algorithmic aspects of the data-driven method SINDy (Sparse Identification of Nonlinear Dynamics) [3] for the identification of the dynamics of Itô SDEs and SDDEs with a single discrete delay. We use single-path reconstructions to obtain time-series data of the stochastic process and different Itô-Taylor based estimators to obtain the intrisic drift and diffusion functions [4]. We present a comparative computational analysis on some SDEs and SDDEs models testing this single-path approach in combination with all the estimation strategies [1][2]. This work falls within the activities of PRIN-MUR 2022 project “Stochastic numerical modelling for sustainable innovation”, CUP: E53D23017940001, granted by the Italian Ministry of University and Research within the framework of the Call relating to the scrolling of the final rankings of the PRIN 2022 call.

[1] Breda, D., Conte, D., D’Ambrosio, R., Santaniello, I., Tanveer, M. (2026) Sparse Identification of Nonlinear Dynamics for Stochastic Delay Differential Equations. J. Comput. Appl. Math., Vol. 479, pp. 117247.
[2] Breda, D., Conte, D., D’Ambrosio, R., Santaniello, I., Tanveer, M. (Submitted) A Matlab code for discovering governing dynamics in Stochastic Differential Equations using SINDy algorithm and Itô-Taylor based approximation.
[3] Brunton, S.L., Proctor, J.L., Kutz, J.N. (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS, Vol. 113, pp. 3932-3937.
[4] Wanner, M., Mezic, I. (2024) On Higher Order Drift and Diffusion Estimates for Stochastic SINDy. arXiv:2306.17814.

Speaker: Ida Santaniello (University of Salerno)

17:15 A Conservative IMEX schema for Tumor Angiogenesis: Model, Analysis, and Efficient Simulation

We present a mathematical and computational framework for the numerical simulation of tumor-induced angiogenesis, a process of central relevance in sustainable healthcare modeling and cancer treatment planning. The continuous model consists of a five-component PDE system coupling endothelial cell density $C$, protease concentration $P$, inhibitor concentration $I$, extracellular matrix density $F$, and oxygen concentration $O$, where oxygen acts as a key regulator of vascular growth through Michaelis-Menten kinetics. Existence, uniqueness, boundedness of solutions, and the existence of a global attractor are established analytically (De Luca and Marcellino, 2025).

For the numerical solution, we develop a conservative implicit-explicit (IMEX) Modified Patankar method that overcomes a fundamental limitation of standard discretisations: the violation of solution positivity near steep gradients or when concentrations approach zero. The scheme treats diffusion implicitly via Crank-Nicolson and handles chemotaxis and reaction terms through a Modified Patankar formulation built on a novel \emph{flux-based production-destruction decomposition}. Interfacial fluxes are uniquely defined at cell boundaries via upwinding, ensuring discrete mass conservation; both production and destruction terms are weighted by Patankar denominators, yielding a genuine Modified Patankar scheme in the sense of Burchard, Deleersnijder, and Meister (2003). Positivity preservation is proven under a mild diffusive CFL condition.

The resulting method is first-order in time and second-order in space. Numerical experiments on the five-component angiogenesis model confirm the theoretical predictions: the scheme preserves positivity without a single violation across all test scenarios, including stress tests with near-zero initial data and time steps exceeding the CFL limit by a factor of $50$. In practical simulations, the IMEX-Patankar method permits time steps up to two orders of magnitude larger than fully explicit Runge-Kutta integration, achieving a measured speed-up of approximately $26\times$ in the number of time steps on the reference angiogenesis benchmark with $M=256$ grid points.

Speaker: Pasquale De Luca (Università di Napoli Parthenope)

16:15 → 18:00 MS14 - Mechanics of Metamaterials: from Modeling to Applications

16:15 The role of anisotropic homogenized mass in locally resonant metamaterials

Locally resonant metamaterials have attracted a lot of interest in recent years thanks to their capability to manipulate elastic waves. They typically consist of periodically distributed resonant elements, e.g. soft inclusions in a stiff matrix, that interact with the propagating wave, leading to the formation of band gaps, which can be interpreted as an interval of negative homogenized mass.

When inclusions lack rotational symmetry, the homogenized mass density of the media becomes anisotropic and lead the formation of polarization bands. This allows the achievement of new capabilities in wave manipulation, such as selective wave polarization, mode conversion [1] and negative refraction [2].

Asymptotic homogenization has been proved to be a useful tool to characterize the dynamic properties of locally resonant metamaterials [3,4]. In this work, we make use of such a technique to study the role played by the mass anisotropy in the dispersion properties of the metamaterial, with particular emphasis on the formation of polarization bands. The possibility of selectively polarize and converting elastic waves is then discussed with the aid of some analytical and numerical examples.

[1] G. Ma et al., Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials. Nature Communications 7, 2016.
[2] G. Bonnet and V. Monchiet, Negative refraction of elastic waves on a metamaterial with anisotropic local resonance. Journal of the Mechanics and Physics of Solids 169, 2022.
[3] C. Comi and J.J. Marigo, Homogenization approach and Bloch-Floquet theory for band-gap predictions in 2D locally resonant metamaterials. Journal of Elasticity 139, 2020
[4] D. Faraci et al., Wave polarization control in anisotropic locally resonant materials. Applied Sciences 13, 2023.

Speaker: David Faraci (Politecnico di Milano)

16:30 Stability domains of chiral periodic lattices

In recent years, metamaterials have received a great deal of research attention due to their potential for energy dissipation. Their ability to finely tune critical modes and to harness non-Eulerian instability mechanisms (such as snap-through) opens the way to substantial energy absorption while preserving elastic reversibility. Remarkably, these dynamic and dissipative characteristics are not intrinsic but can be precisely engineered through deliberate manipulation of the material microgeometry.
In this work, a metamaterial featuring generic rigid finite-sized joints has been investigated. The lattice is represented as a grid of shearable and flexible beams interconnected by rigid components and, by employing Bloch-Floquet theory, the closed-form expression of the stability domain and the associated critical modes have been analytically derived. By suitably selecting the geometric parameters of the rigid joints, it becomes possible to tailor a broad spectrum of critical modes under different macro-stress states, enabling the onset of microscopic critical modes before the macroscopic ones. It is emphasized that, in this metamaterial, chirality influences only the micro-critical state, while leaving the macro critical state unaffected. The analytical findings have been subsequently compared with FEM simulations and experimental tests conducted on 3D-printed specimens, revealing a good level of agreement.

References
[1] Marasciuolo, N., De Tommasi, D., Trentadue, F., Vitucci, G., Tailored multiscale instabilities in a grid metamaterial, Extreme Mechanics Letters, 75, 102284, 2025.
[2] Trentadue, F., Caramia, G., De Tommasi, D., Marasciuolo, N., Vitucci, G., Elastic stability of a lattice of cross-braced shear deformable beams, European Journal of Mechanics-A/Solids, 102, 105118, 2023.
[3] Trentadue, F., De Tommasi, D., Marasciuolo, N., Stability domain and design of a plane metamaterial made up of a periodic mesh of rods with cross-bracing cables, Applications in Engineering Science, 5, 100036, 2021.

Speaker: Nicola Marasciuolo (Politecnico di Bari)

16:45 A numerical framework to describe anisotropic plastic behaviour of homogenized lattice metamaterials

Homogenization of lattice metamaterials enables modelling lattice cells as equivalent solid structures with anisotropic mechanical properties. This aspect enables performing preliminary structural analysis of mechanical components made of metamaterials without modelling the entire lattice cells thus saving computational cost. Elastic homogenization has been widely explored in the literature and many works identified elastic homogenized mechanical properties. On the contrary, elastic-plastic homogenization remains an open field, and it consists of modelling the anisotropic homogenized hardening behaviour of the cells. In this work the authors propose a mathematical framework to describe the anisotropic homogenized hardening behaviour of both 3D and 2D lattice cells. Finite element simulations were implemented by using the periodic boundary conditions, and, firstly, homogenized elastic properties were obtained. After, Hill yielding criterion, Levy-Mises plastic flow rule and a reference homogenized plastic curve along one of the directions of anisotropy were combined to describe the plastic homogenized properties. In particular, a scaling procedure was introduced, and this latter consisted of identifying Hill coefficients by scaling the homogenized plastic curves along the various directions of anisotropy to match the reference plastic curve, and the procedure was implemented in a plane with Hill equivalent stress and plastic strain on y and x axes, respectively. The proposed framework was validated both numerically and experimentally. The first validation was performed by comparing the tensile curves obtained by simulating the homogenized model and the whole lattice structures, while the second validation was performed through mechanical tests on manufactured graded lattice specimens. During mechanical tests digital image correlation (DIC) was also used for an adequate measure of the strains of lattice units. Different materials, i.e. polymeric and metallic, were considered for the manufacturing of the specimens, and the obtained results demonstrated a good overlap between experimental, numerical homogenized and numerical lattice results.

Speaker: Lorenzo Romanelli (University of Trento)

17:00 Multiple tensile restabilisation from the homogenisation of a two-dimensional network of prestressed Reissner rods

Quasi-static homogenisation of two-dimensional periodic networks of elastic rods provides an effective approach to characterising the mechanical properties of the corresponding equivalent continua. In particular, the macroscopic response of the homogenised material can be tailored by tuning the geometrical and mechanical parameters of the underlying network [1,2].
Unusual mechanical behaviours have been reported in this context, including bounded stability domains in the prestress plane for prestressed elastic grids equipped with concentrated sliders [3], and tensile restabilisation in prestressed axially deformable grids [4].

However, the stability of grids composed of prestressed, axially deformable, and shearable rods — and of their homogenised continua — has not yet been investigated.

In this talk, we consider a rectangular network of prestressed Reissner rods, connected by rigid joints of tunable length. The stability domains of both the discrete network and its homogenised elastic continuum are determined and represented in the $p_1-p_2$ prestress plane. The results reveal multiple tensile restabilisation islands beyond the first bifurcation (Figure 1).

References

[1] Franzoi, M., Bigoni, D., Piccolroaz, A. (2026) Homogenization of architected materials incorporating shearable beams. International Journal of Engineering Science, 218:104397
[2] Viviani, L., Bigoni, D., Piccolroaz, A. (2024) Homogenization of elastic grids containing rigid elements. Mechanics of Materials, 191:104933.
[3] Bordiga, G., Bigoni, D., Piccolroaz, A. (2022) Tensile material instabilities in elastic beam lattices lead to a bounded stability domain. Phil. Trans. R. Soc. A, 380:20210388.
[4] Bigoni, D., Piccolroaz, A. (2025) Material instability and subsequent restabilization from homogenization of periodic elastic lattices. Journal of the Mechanics and Physics of Solids, 200:106129.

Speaker: Matteo Franzoi (University of Trento)

17:15 Model-Driven Digital Volume Correlation for Large-Deformation Experiments on Pantographic Metamaterials

Mechanical metamaterials with periodic mesostructures pose severe challenges for full-field measurement techniques when subjected to large deformations. In this contribution, we present a model-driven Digital Volume Correlation (DVC) strategy that tightly couples continuum modeling with experimental analyses of pantographic metamaterials tested within a tomographic chamber.

At the macroscale, pantographic blocks are modeled as second-gradient continua, providing predictions for the displacement of a set of representative material points, chosen as the centers of hinges or pivots in the underlying architecture. These predictions are then used, via static condensation, to construct a mechanically consistent initial guess for a finite-element-based DVC scheme, which is subsequently refined by minimizing gray-level residuals with suitably tuned mechanical regularization.

The approach is applied to in situ three-point bending tests on 3D-printed pantographic blocks with both deformable hinges and perfect pivots, investigated under extreme loading conditions where imposed displacements reach a significant fraction of the specimen size. Non-incremental DVC analyses initialized by the model-driven procedure successfully reconstruct the deformed configurations, and comparisons with incremental DVC using intermediate scans show very close agreement in terms of displacement fields and gray-level residuals.

These results demonstrate that embedding suitable second-gradient models within DVC workflows enables reliable experimental quantification of complex deformation mechanisms in architected metamaterials, while also reducing computational cost and enlarging the range of experimentally accessible loading paths.

Main reference:
Ciallella, A., Murcia Terranova, L., Smaniotto, B., Vintache, A., Hild, F., Model-driven digital volume correlation: A step forward in experimental analyses of metamaterial deformations. Mathematics and Mechanics of Solids, 10812865251386430.

Speaker: Alessandro Ciallella (Università dell'Aquila)

17:30 Effective Micromorphic Modeling of Metamaterial Behavior

The intricate architectures of phononic crystals and metamaterials induce sophisticated wave behaviors that are directly tied to their internal geometries. While high-fidelity numerical models resolve these effects accurately, the computational overhead becomes prohibitive during extensive time-domain studies. To bridge this gap, effective continuum frameworks have emerged as a way to simulate macroscopic responses while embedding essential microscale physics [1,2]. This work evaluates the performance of micromorphic representations by benchmarking them against direct simulations of discrete microstructures. By identifying where these models succeed and where they diverge, we establish clearer boundaries for their use in the predictive design of advanced engineering materials.

[1] G. Rizzi, M.V. d’Agostino, J. Voss, D. Bernardini, P. Neff, A. Madeo (2024). From frequency-dependent models to frequency-independent enriched continua for mechanical metamaterials. European Journal of Mechanics-A/Solids, 106, 105269.

[2] J. Voss, G. Rizzi, P. Neff, A. Madeo (2023). Modeling a labyrinthine acoustic metamaterial through an inertia-augmented relaxed micromorphic approach. Mathematics and Mechanics of Solids, 28(10), 2177-2201.

Speaker: Gianluca Rizzi (TU Dortmund)

17:45 Pseudospectral Stability Analysis of Wave Propagation in Microstructured Materials with Vector-Valued Phase Fields

We investigate the propagation of elastic waves with time-varying amplitudes in solids with "active" microstructure described by vector-valued phase fields. Depending on the constitutive choices adopted for the microstructural actions, the linearized evolution equations involve a non-normal matrix.
The spectra of non-unitarily diagonalizable matrices can be extremely sensitive to small perturbations in the matrix entries, making stability predictions based solely on spectral analysis unreliable, especially when uncertain constitutive parameters vary.
To obtain a more robust characterization of the dynamical response, we analyze the pseudospectrum of the associated operators, distinguishing between complex perturbations related to finite-precision computations and structured perturbations reflecting uncertainties in the values of the material parameters.
As a case study, we consider the linearized dynamics of quasicrystals, metallic alloys characterized by quasicrystalline symmetry groups. For these materials, the phase field, or phason field, represents atomic rearrangements that ensure the quasiperiodicity of the lattice. In particular, we investigate the influence of a microstructural self-action on the stability of elastic wave propagation through a parametric analysis. The results show that, for some specific choices of the phason self-action, the eigenvalues of the matrix are highly sensitive to small variations in the constitutive parameters, and that the structured pseudospectrum predicts instability of the material, whereas spectral analysis indicates, instead, stability.

Speaker: Daniele La Pegna (Scuola Normale Superiore)

20:00 → 23:00 Cena sociale

To participate, follow the instructions available here: https://events.dm.unipi.it/event/331/page/51-social-events

Thursday 4 June

09:00 → 09:45 Plenary talk: Modelling the multiphysics of the human eye

The research presented in this talk investigates the multiphysics modelling of the human eye through a set of dedicated, tissue-specific studies regarding cornea, iris, vitreous body, and retina. Each ocular component is analysed independently isolating its dominant physical mechanisms. The cornea is modelled as a layered, anisotropic soft tissue, with particular emphasis on stromal collagen architecture and its influence on nonlinear, hyperelastic mechanical behaviour under intraocular pressure and external loading. Microstructure-informed constitutive formulations are employed to connect collagen organisation to macroscopic stress and deformation. The iris is examined as an active elastic fiber reinforced structure, where geometry and material response govern pupil dynamics and anterior segment mechanics. The vitreous body is described as a poro-elastic medium, capturing its role in load transmission, damping, and mechanical interaction with surrounding tissues. The retina is modelled as a thin, layered structure, composed by structural element with distinct mechanical properties, focusing on deformation, stress localisation, and interaction with the vitreous under physiological and pathological conditions. All together, these separated yet conceptually aligned studies define a coherent multiphysics perspective on ocular mechanics. The proposed modelling framework provides tissue-specific insight and lays the groundwork for future integrated simulations, disease modelling, and clinically oriented applications.

Speaker: Anna Pandolfi (Politecnico di milano)

09:45 → 10:15 Junior plenary talk: Isogeometric methods for the study of fracture mechanics via phase-field modelling

Fracture mechanics remains one of the most challenging and impactful research areas in engineering. The ability to accurately predict fracture phenomena is essential for the safe and efficient design of structural systems, with profound economic, environmental, and societal implications. Preventing structural failure reduces maintenance costs, material losses, environmental hazards associated with catastrophic spills, and the loss of human life.
The foundations of modern fracture mechanics can be traced back to the seminal work of Griffith [1], who introduced the energetic interpretation of fracture and the concept of fracture energy associated
with crack evolution. Since then, the continuous growth of computational capabilities has driven the development of increasingly sophisticated numerical approaches for fracture analysis.
Among these, phase-field methods have emerged as one of the most powerful and versatile frameworks for the simulation of complex fracture processes. Their main strength lies in the ability to represent crack evolution through a continuous description of discontinuous interfaces, naturally handling complex crack topologies without ad-hoc tracking strategies.
Within this framework, the accurate modeling of fracture energy dissipation plays a central role. In recent years, high-order phase-field formulations have attracted growing attention due to their enhanced regularity properties and their potential to significantly improve computational efficiency and solution accuracy [2]. The resulting high-order partial differential equations find a particularly suitable discretization environment in Isogeometric Analysis [3], whose high-continuity basis functions provide a natural framework for their numerical treatment.
This talk will discuss recent advances in high-order phase-field models for fracture, with particular emphasis on both static and dynamic regimes [4]. Special attention will be devoted to the interplay between variational modeling, numerical efficiency, and predictive capabilities, highlighting how high-order formulations can substantially reduce computational costs while preserving remarkable accuracy in the simulation of complex fracture phenomena.

References
[1] Griffith, A. A., Taylor, G. I. VI. e phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 221, 163-198, 1921.
[2] Greco, L., Maggiorelli, E., Patton, A., Negri, & Reali, A. AT1 fourth-order isogeometric phase-field modeling of brittle fracture. Mathematical Models and Methods in Applied Sciences, 13, 2741-2795, 2025.
[3] Hughes, T. J., Cottrell, J. A., & Bazilevs, Y. Isogeometric analysis: CAD, finite elements, NUReBS, exact geometry and mesh refinement. Computer methods in applied mechanics and engineering, 194(39-41), 4135-4195, 2005.
[4] Greco, L., Kiendl, J., Patton, A., Negri, & Reali, A. Fourth-order isogeometric phase-field modeling of dynamic brittle fracture: Numerical study and comparison with second-order models. Computer methods in applied mechanics and engineering, 449, 118513, 2026.

Speaker: Luigi Greco (University of Pavia)

10:15 → 10:45 Junior plenary talk: Computational modeling and simulation of advanced bioprinting techniques

This work presents a computational framework for the optimization of extrusion-based bioprinting processes, with particular emphasis on standard and coaxial bioprinting technologies. Extrusion-based bioprinting is widely used for the fabrication of biomimetic structures containing living cells, thanks to its ability to process a broad range of biomaterials and bio-inks. However, the quality of the printed constructs strongly depends on the complex rheological behavior of the bio-inks, which directly affects printability, cell viability, and shape fidelity. In particular, coaxial bioprinting introduces additional challenges related to fluid–fluid interactions and interface stability, making process optimization particularly difficult.
The study addresses the problem from a dual perspective, considering both the flow inside the extruder and the dynamics of the material after extrusion. Inside the nozzle, a reduced-order predictive model is developed to correlate key process parameters — including nozzle diameter, extrusion pressure, and flow rate — with the stresses acting on embedded cells and the resulting cell viability. The framework is further translated into practical graphical tools to support rapid process design and parameter selection.
Outside the nozzle, the extrusion process is formulated as a viscoelastic free-surface flow problem, extended to coaxial bioprinting through a multiphase approach. An Arbitrary Lagrangian–Eulerian (ALE) finite element framework is implemented to capture phenomena such as die swell, filament evolution, and interfacial stresses between core and shell fluids.
Numerical simulations are used to investigate the influence of rheological and viscoelastic parameters on printing resolution and stress distribution in both standard and coaxial configurations, providing predictive tools for the design and optimization of advanced bioprinting processes.

References
1. Chirianni, F., Vairo, G., Marino, M. (2024). Development of process design tools for extrusion-based bioprinting: From numerical simulations to nomograms through reduced-order modeling. Computer Methods in Applied Mechanics and Engineering, 419, 116685.
2. Chirianni, F., Vairo, G., Marino, M. (2024). Influence of extruder geometry and bio-ink type in extrusion-based bioprinting via an in silico design tool. Meccanica, 59(8), 1285-1299.

Speaker: Francesco Chirianni (Università di Roma Tor Vergata)

10:45 → 11:15 Coffee break

11:15 → 12:45 MS03 - Graph Neural Networks for Computational Physics

11:15 Learning Vascular Hemodynamics: Physics-Informed GNNs Inference from Capillary Networks to Pulsatile Flow

Simulating microvascular blood flow in anatomically realistic networks remains a formidable computational task. The intrinsic multiscale structure of the vascular system, the geometric heterogeneity of capillary beds, and the nonlinear rheological behavior of blood in the microcirculation jointly lead to highly complex mathematical models whose direct numerical solution is often prohibitively expensive.

In this work, we propose a graph-based, physics-informed learning framework that exploits graph neural networks (GNNs) trained on synthetically generated microvascular graphs to approximate pressure and velocity fields with high efficiency. The approach integrates stochastic generative algorithms for vascular network construction with a physics-driven loss formulation enforcing mass conservation and rheological consistency. By embedding these domain-specific inductive biases into the learning process, the surrogate model preserves the governing physical structure while significantly reducing computational cost.

The resulting GNN architecture exhibits strong generalization capabilities across heterogeneous microvascular topologies and accurately reproduces full-order solutions under both linear and nonlinear rheological regimes. Substantial computational speedups are achieved without compromising predictive fidelity. Validation experiments conducted on anatomically reconstructed mouse cortical microvasculature further demonstrate the scalability, robustness, and reliability of the method in realistic settings.

As a natural extension, we address time-dependent hemodynamics. We introduce a complementary GNN architecture designed to reconstruct periodic flow regimes and to propagate pulsatile pressure and velocity dynamics across successive cardiac cycles on vascular graphs. The integration of steady and time-periodic formulations highlights the versatility of physics-informed graph learning for modeling complex vascular phenomena. Overall, the proposed framework provides a scalable and efficient paradigm for real-time simulation of both stationary and pulsatile microvascular blood flow, paving the way for advanced multiscale vascular modeling and biomedical applications.

Speaker: Paolo Botta (MOX, Department of Mathematics, Politecnico di Milano)

11:30 Graph-Based Nonlinear Reduced-Order Modeling for Time-Domain Electromagnetics

Numerical modelling plays a crucial role in revealing the behaviour of light and matter interactions at the nanoscale, exploiting computational schemes such as the Discontinuous Galerkin Time-Domain (DGTD) method. Given the computational complexity associated to this task, we study reduced-order modelling (ROM) due to the pressing need for fast surrogate models capable of handling physically and geometrically parametrized electromagnetic problems. Traditional ROM techniques like Proper Orthogonal Decomposition (POD) and Greedy algorithm have already been investigated in the literature, along with their inherent limitations in effectively capturing nonlinear phenomena. Here, we exploit a deep learning-based ROM strategy showing promising potential, the Graph Convolutional Autoencoder (GCA) method, serving as a nonlinear extension of POD compression, harnessing the power of Graph Neural Networks to induce a geometric bias in the learning process when dealing with complex and unstructured meshes. We propose a fully data-driven nonlinear ROM extending the GCA method tailored for time-domain electromagnetics, fully exploiting the training dataset of high-order (in space and time) DGTD snapshots, and the spectral quantities of interest. We explore the use of advanced latent-space propagators to better capture the high-frequency behaviour of electromagnetic problems. This direction aims to unlock faster and more accurate surrogate models for time-domain electromagnetics, especially for applications requiring complex geometries, in the context of inverse design and optimization.

Speaker: Carlotta Filippin (Université Côte d'Azur, Inria, CNRS, LJAD)

11:45 Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs

Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs) [1].
However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding geometric information.
In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN) [3], a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned on external inputs and parameters [2].
The temporal evolution is modeled in the latent space and advanced through time-stepping, allowing for time-extrapolation, and the trajectories are consistently decoded onto geometrically parametrized domains using a GNN.
Our framework enhances interpretability by enabling the analysis of reduced dynamics and supports zero-shot prediction through latent interpolation.
The methodology is mathematically validated via a universal approximation theorem for encoder-free architectures, and numerically tested on complex computational mechanics problems involving physical and geometrical parameters, including the detection of bifurcating phenomena for Navier-Stokes equations.

References:
[1] Federico Pichi, Beatriz Moya, and Jan S. Hesthaven. “A graph convolutional autoencoder approach to model order reduction for parametrized PDEs”. In: Journal of Computational Physics 501 (Mar. 2024), p. 112762. DOI: 10.1016/j.jcp.2024.112762.
[2] Francesco Regazzoni et al. “Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks”. en. In: Nature Communications 15.1 (Feb. 2024), p. 1834. DOI: 10.1038/s41467-024-45323-x.
[3] Lorenzo Tomada, Federico Pichi, and Gianluigi Rozza. Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs. arXiv:2601.11259 [cs]. DOI: 10.48550/arXiv.2601.11259.

Speaker: Lorenzo Tomada (SISSA)

12:00 Coupling Phisically Informed Graph Neural Networks with External Solvers

Machine Learning (ML) methods for solving Partial Differential Equations (PDEs) have recently undergone unprecedented development. Physics-Informed Neural Networks (PINNs) have gained significant attention for their ability to integrate underlying physics into learning frameworks. However, classic PINNs rely on Automatic Differentiation (AD) to compute physics-based loss terms. During backpropagation, AD generates large tensors that increase training overhead and slow the optimization process.

Furthermore, PINNs based on Deep Neural Networks (DNNs) often lack geometric adaptability. This limitation makes them suitable for structured regular grids rather than complex geometries.

The challenge of reducing the computational overhead due to AD has been tackled using external solvers to compute the discrete residual associated to the target equation and using such a residual in a physics informed loss. Graph Neural Networks (GNNs) have been proved to solve the limitations of DNN based approaches, performing well in contexts where geometric adaptability is the key.

We present a novel approach that couples a Graph Neural Network framework with an external numerical solver. This model pairs the superior geometric adaptability of GNNs with the reduced training overhead of external solvers. By using an external solver, our framework eliminates the complications represented by AD in graph aggregation and message passing contexts. The implementation bridges Python-based GNN architectures with a high-performance C++ solver.

This talk covers our model's architecture, mathematical properties, examples, applications, and use cases with a particular focus on Computational Fluid Dynamics (CFD).

Speaker: Niccolò Picchiarelli (Sant'Anna School of Advanced Studies)

12:15 Physics Informed Graph Neural Networks for Nonlinear Dynamics

Deep learning architectures have recently been investigated for fast prediction in parametric PDEs. Within the Model Order Reduction (MOR) paradigm, an offline stage projects the nonlinear solution space into a low-dimensional manifold, and the compressed latent representation enables rapid, accurate predictions with a small computational cost.
In particular, Graph Neural Networks have shown high adaptability to exploit topological informations in modeling high-dimensional dynamical systems governed by partial differential equations on irregular meshes.
We propose a geometry-informed surrogate for nonlinear flow dynamics in which the metric and manifold structure are encoded via a Laplacian eigenvectors embedding, while discrete topological representations are preserved by permutation invariant message-passing on undirected graphs. We also use the Laplacian basis to perform a Graph Fourier transform, enabling spectral filtering of node features.
Dimensionality is reduced through error-guided supernodes selection, to aggregate informations towards high-error regions.
A multiscale, geometry-aware graph autoencoder is trained to learn a compact latent solution manifold. We then integrate the latent dynamics with a Neural ODE, yielding stable long-horizon rollouts and improved generalization across domains and Reynolds regimes.
We perform Data Assimilation directly in the latent space using a Deterministic Ensemble Kalman Filter update. The observation operator is the decoder, so corrections are geometrically consistent with the original solution manifold.
Preliminary experiments on 2D unsteady flows with $Re\in [100,1000]$ indicate that the Laplacian eigenvector features reduce the amount of training data needed to achieve smooth, geometry-consistent reconstructions; the latent space continuous dynamics provides long-horizon stability, reducing error accumulation, and the EnKF updates perform online data assimilation, using sparse sensor observations with quantified uncertainty to correct residual drift.

Speaker: Gennaro Calandriello (Scuola Superiore Sant'Anna)

12:30 Physics-constrained identification of graph-based thermal networks for spacecraft digital twins

Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To solve this challenge,
we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions.
Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization.
The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons. The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise.
The proposed framework provides a principled approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The resulting models are computationally efficient and suitable for integration in spacecraft thermal Digital Twin applications.

Speaker: Luca Sosta (Politecnico di Milano)

11:15 → 12:45 MS04.2 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

11:15 Adaptive Isogeometric Analysis of the Cahn--Hilliard Equation with THB-splines

Isogeometric Analysis has been proven to be a suitable tool for the discretization of higher-order formulations describing phenomena like brittle fracture or phase separation in fluid mixtures [1,2]. In this context, phase-field models constitute a convenient approach to model sharp interface problems, since they incorporate a continuous field variable --the field order parameter-- to describe the transition between the phases, allowing for an automatic tracking of the evolution of the smooth interfaces. From a computational standpoint, phase-field models need fine meshes, at least locally, in order to accurately resolve the phase-field profile. This factor becomes particularly critical in volumetric domains, where the computational cost is a major concern.

We present a higher-order adaptive isogeometric framework for volumetric phase-field problems, exemplified by the Cahn--Hilliard equation. Truncated Hierarchical B-splines (THB-splines) provide a flexible basis supporting local refinement and coarsening [3,4], enabling efficient resolution of evolving interfaces in 2D and 3D. Our adaptive scheme automatically refines the mesh at phase interfaces and coarsens it in the bulk, with solution transfer between successive meshes handled via a quasi-interpolation operator that is parallelizable and computationally efficient. We demonstrate the effectiveness of this approach through numerical studies that highlight the method’s ability to accurately track interfaces, illustrating the advantages of mesh adaptivity in complex volumetric phase-field simulations.

Speaker: Lucas Venta Viñuela (University of Pavia)

11:30 A Cahn–Hilliard Equation-based Tumor Growth Model with Nutrient Coupling

Predicting tumor dynamics in biological systems under physiologically relevant conditions remains a challenging problem for mathematical and computational modeling. Among the various approaches proposed to describe tumor dynamics, phase-field (diffuse-interface) formulations provide an attractive continuum modeling framework to capture the spatiotemporal evolution of interfaces separating phases and integrate multiple physical processes and interacting species into a unified description of complex multiphysics phenomena. Within this framework, this work presents a Cahn–Hilliard (CH) equation-based tumor growth model that governs tumor–healthy tissue interactions under the influence of nutrient concentration. The formulation involves a fourth-order differential operator that imposes higher continuity requirements on approximation spaces for a well-defined primal variational formulation. We use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions within a unified geometric and analysis framework. Furthermore, a locally adaptive IGA scheme with truncated hierarchical B-splines is used to reduce computational cost while maintaining accuracy, since phase-field models often demand fine meshes to resolve steep gradients at phase interfaces. The model is first validated on standard benchmark cases and subsequently applied to a patient-specific, organ-scale breast model reconstructed from magnetic resonance imaging (MRI) data. The results capture the characteristic tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments also shows the diversity of tumor dynamics produced by different model parameter choices. Taken together, the findings demonstrate the predictive potential of the CH phase-field tumor growth model integrated with a locally adaptive IGA framework.

Speaker: Dhiraj Sanghavijay Bombarde (Department of Civil Engineering and Architecture, University of Pavia, Italy)

11:45 Parameter optimization for the Cahn-Hilliard equation with applications to tumor growth models

The Cahn-Hilliard equation is used to describe the dynamics of two phases interacting across a thin region known as the interface. This framework naturally lends itself to the formulation of tumor growth models.
In this work we deal with parameter estimation for a phase-field model of tumor evolution coupled with nutrient dynamics. The mathematical model consists of a Cahn-Hilliard type equation describing the tumor phase field coupled with a diffusion equation for the nutrient concentration, including chemotactic effects and reaction terms. The resulting system captures key mechanisms such as tumor proliferation, nutrient consumption and chemotactic interactions.

The forward problem is solved numerically using isogeometric analysis with second order B-spline basis functions, which naturally provide the $C^1$ regularity required by the fourth-order operator appearing in the Cahn-Hilliard equation. Time integration is performed using a generalized-$\alpha$ scheme combined with Newton iterations to handle nonlinearities.
The inverse problem is formulated as a PDE-constrained optimization problem aimed at identifying model parameters from observed tumor configurations. The gradient of the objective functional is computed through sensitivity equations derived from the linearization of the governing system. The resulting optimization algorithm combines a weighted gradient descent and a quasi-Newton method with Gauss-Newton Hessian approximation.

The proposed framework provides a computational approach for calibrating phase-field tumor growth models and represents a step toward patient-specific simulations based on medical imaging data.

Speaker: Leonardo Beretta (Università di Pavia)

12:00 Local h-, p-, and k-Refinement Strategies for the Shifted Boundary Method with THB-Splines

Trimming and immersion techniques have become standard tools for handling complex geometries in isogeometric analysis (IGA). By decoupling the physical domain from the computational background mesh, mesh generation is simplified compared to body-fitted approaches. However, this embedding strategy introduces numerical challenges, including ill-conditioning due to small cut elements.
The Shifted Boundary Method (SBM) addresses these issues by restricting the computational domain to uncut elements and imposing boundary conditions through a Taylor expansion from a surrogate boundary to the true boundary. For Neumann conditions, the flux evaluation requires higher-order derivatives in the Taylor expansion, which effectively reduces the achievable convergence rate by one order.
This contribution investigates, for the first time, the combination of the SBM with Truncated Hierarchical B-splines (THB-splines). We systematically study local h-, p-, and k-refinement strategies and analyze their influence on accuracy, stability, and computational efficiency in trimmed domains. In addition to the standard shift operator, we introduce an enhanced formulation that incorporates mixed partial derivatives within the Taylor expansion.
Benchmark problems are used to evaluate the convergence behavior under different refinement strategies. The results indicate that local degree elevation can compensate for the loss of optimal convergence rates associated with Neumann boundary conditions in the classical SBM.
The study clarifies the role of refinement strategies in trimmed IGA formulations and provides guidance for the robust application of SBM in locally refined spline discretizations.

Speaker: Christoph Hollweck (OTH Regensburg/ TU München)

12:15 A p-adaptive high-order polytopal method for modelling neuronal electrophysiology

Traveling wave-like phenomena arise in a wide range of biological processes, including electrical signal propagation in the nervous system and brain tissue. Accurately simulating these phenomena poses significant numerical challenges, as sharp and rapidly moving wavefronts require high spatial and temporal resolution to be properly captured. Such requirements often lead to prohibitive computational costs, especially in large and heterogeneous domains. The evolution of the transmembrane potential is governed by steep, fast wavefronts propagating across multiple brain regions, often following preferential axonal pathways. These dynamics emerge from complex multiscale interactions, where rapid ionic exchanges at the cellular level generate electrical signals that propagate through anisotropic and heterogeneous tissues. High-order discontinuous Galerkin methods on polygonal and polyhedral meshes (PolyDG) offer great flexibility and accuracy for such problems, but their computational cost can remain significant when uniform high-order discretizations are used. To address this limitation, we propose a p-adaptive PolyDG strategy that exploits the solution's intrinsic traveling-wave structure. In particular, the transmembrane potential exhibits strong spatial variations localized near the propagating wavefront, while the solution remains nearly stationary elsewhere. Our approach consists of designing efficient a posteriori error indicators that accurately detect the wavefront location. These indicators drive fully automatic local adjustment of the polynomial degree, allowing higher-order approximations only where they are truly needed. We present numerical results that validate the effectiveness of the proposed method and demonstrate its application to the simulation of epileptic events in heterogeneous brain domains, including grey and white matter. The results show that polynomial adaptivity significantly reduces the total number of degrees of freedom and the overall computational cost while maintaining high-order accuracy throughout the simulation.

Speaker: Caterina B. Leimer Saglio (Politecnico di Milano)

12:30 A high–order time and space–accurate method for the explicit dynamics of geometrically exact beams

In this contribution, we propose a high–order time and space–accurate isogeometric collocation (IGA-C) method for the explicit dynamics of geometrically exact beams [1]. While high–order accuracy in space is a well established feature of IGA-C for both explicit and implicit dynamics of geometrically exact beams [2, 3], time accuracy is still restricted to second–order. For some applications where temporal error is dominant, .e., impact and crash dynamics, such a lower order accuracy represents a significant drawback that prevents a fully exploitation of the high–order IGA-C potentialities. We fill this gap by proposing a high–order (up to sixth) time–accurate method based on the Runge-Kutta-Munthe-Kaas time integrator [3]. Exploiting the analogy between the dynamics of rigid bodies and shear deformable beams, we recast the classical Runge-Kutta scheme to solve the nonlinear governing equations evolving on the beam configuration manifold, IR3 × SO(3). Numerical applications to challenging benchmark problems will show the capabilities of the proposed formulation to achieve high–order time and space accuracy, while preserving computational efficiency.

References

[1] G. Ferri and E. Marino, A. Reali, G. Sangalli, Explicit high-order time and space accurate isogeometric collocation method for the dynamics of geometrically exact beams, Comput Methods Appl. Mech. Eng., Vol. 449, pp. 118495, 2026.
[2] E. Marino, J. Kiendl, L. De Lorenzis, Explicit isogeometric collocation for the dynamics of three-dimensional beams undergoing finite motions,Comput. Methods Appl. Mech. Eng., Vol. 343, pp. 530-549, 2019.
[3] E. Marino, J. Kiendl, L. De Lorenzis, Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions, Comput Methods Appl. Mech. Eng.,Vol. 356, pp. 548-570, 2019.
[4] H. Munthe-Kaas, High order Runge-Kutta methods on manifolds, Applied Numerical Mathematics, Vol. 29, pp. 115–127, 1999.

Speaker: Giulio Ferri (Universittà degli Studi di Firenze)

11:15 → 12:45 MS06.2 - Numerical Modeling for Sustainability Problems

11:15 Space-Time Energetic Boundary Element Method for Mixed 3D Elastodynamic Problems

To further advance the regularisation and numerical treatment of the double-layer operator in three-dimensional elastodynamics within the space-time Energetic Boundary Element Method (EBEM) framework [1], this work extends the analysis to the singular behaviour of the adjoint double-layer and hypersingular operators arising in mixed boundary value problems. The mixed formulation is characterised by the simultaneous prescription of displacement and traction conditions on complementary parts of the domain boundary, resulting in a coupled system of time-dependent Boundary Integral Equations (BIEs) involving all four elastodynamic boundary integral operators. By exploiting a suitable decomposition of the traction-displacement and traction-traction Green’s functions, a fully regularised system of BIEs is derived. The resulting formulation is discretised using a Galerkin-type EBEM, originally introduced for 3D elastodynamics in [2], combined with exact analytical integrations in the time variable. A central challenge of the proposed approach lies in the efficient and stable evaluation of the remaining weakly singular double integrals in space, whose accurate approximation is essential to ensure the robustness of the mixed formulation. In this context, the space-time integration domains are generally delimited by the wave fronts of primary and secondary elastic waves, resulting in complex geometric configurations. By analyzing the geometric characteristics of these domains, we develop an ad-hoc quadrature strategy, where the outer integrals are computed efficiently by Gaussian quadrature, while the inner integrals are evaluated with respect to polar coordinates and expressed by analytical formulations. The effectiveness of the proposed approach is illustrated via two benchmark problems.

[1] L. Coppolino, L. Desiderio. Space-time energetic Galerkin BEM for the numerical solution of 3D elastodynamic problems: overcoming challenges of the strongly singular integral operator. Comput Mech 76, 1689–1714 (2025).

[2] A. Aimi, S. Dallospedale, L. Desiderio, C. Guardasoni. A space-time Energetic BIE method for 3D Elastodynamics. The Dirichlet case. Computational Mechanics, 72(5), 2023, pp. 885–905.

Speaker: Luciano Coppolino (Università degli Studi di Messina)

11:30 An Exponential Fitting BDF Scheme for Efficient Simulation of Oscillatory Quantum Devices

The accurate numerical modeling of superconducting quantum devices is essential
for advanced computing and sensing technologies. Their governing equations are
nonlinear and often yield highly oscillatory solutions [1, 2], making standard time
integration schemes inaccurate unless very small time steps are used.
We consider a Backward Differentiation Formula (BDF) predictor-corrector method
enhanced through Exponential Fitting (EF) [3]. The idea is to incorporate physically
relevant parameters, such as damping factors and dominant frequencies, directly into
the discrete operator. The EF coefficients are obtained by imposing exactness of the
discrete derivative on a fitted functional space including exponential and oscillatory
modes, thus aligning the scheme with the qualitative behavior of the device.
This structure-aware discretization allows accurate simulations with larger time
steps, reducing computational effort and associated energy consumption while pre-
serving reliability. The approach is particularly effective in multi frequency regimes
typical of SQUID arrays and parametric amplifiers, where conventional solvers may
be overly restrictive.
Numerical tests on benchmark oscillatory problems and superconducting models
show improved accuracy at the same computational cost of standard BDF imple-
mentations, providing an efficient tool for the simulation and design of oscillatory
superconducting devices.

References
[1] N. D. Mermin, Quantum Computer Science: An Introduction, Cambridge Uni-
versity Press, 2007.
[2] C. Guarcello et al., Driving a Josephson Traveling Wave Parametric Amplifier
into chaos, Chaos, Solitons & Fractals, 189, 2024.
[3] L. Gr. Ixaru, Exponential Fitting, Kluwer Academic Publishers, 2004.

Speaker: Roberto Sanfelice (Dipartimento di Matematica/DIPMAT, Università degli studi di Salerno)

11:45 Augmented predictor-corrector PINN for estimating root zone soil moisture from data at shallower depths

The difficulty of installing soil moisture sensors in the deeper layers of the root zone represents a major limitation for both hydrological modeling and irrigation management. In this study, we propose a predictor–corrector Physics-Informed Neural Network (PINN) framework to estimate soil water content at 60 cm depth using solely measurements collected at 30 cm. The predictor–corrector architecture enables a physically consistent data augmentation strategy, whereby additional informative samples are generated over a depth domain spanning from 0 to 60 cm, allowing the transition from Neumann to Dirichlet boundary conditions and the progressive refinement of the predictions through successive training stages. The results show that the reconstructed soil moisture at 60 cm closely reproduces the observed dynamics, highlighting the capability of the proposed approach to recover soil moisture profiles even in the absence of direct measurements. This methodology therefore provides a practical solution for extending observational datasets in real-world applications, particularly when in situ sensors or satellite products are limited to shallow soil layers.

Speaker: Mariateresa Bruni (CNR IRSA, POLITECNICO DI BARI)

12:00 Modeling Non-Stationarity through PDE Penalization: An Application to Mobility Data

Sustainable urban development requires quantitative tools able to describe complex spatio-temporal processes characterized by spatial heterogeneity and directional structure. Classical stationary models are often inadequate for heterogeneous metropolitan areas, where mobility patterns and population density evolve under infrastructure constraints and recurrent temporal cycles.
We propose a semiparametric spatio-temporal regression model in which anisotropy and non-stationarity can be properly modeled through a partial differential equation regularization term. Specifically, this term involves a general second-order linear differential operator, allowing the model to incorporate prior physical knowledge about the phenomenon under study.
In this work, we exploit this flexibility by introducing a spatially varying diffusion term that adapts to the geometry of the domain and captures directional features of the process. From a mathematical perspective, this is achieved by constructing a non-stationary diffusion tensor. Working with tensors raises several challenges, such as preserving positive definiteness when performing operations like averaging or interpolation. To address these issues, we develop a suitable mathematical framework based on the Log-Euclidean metric. This choice preserves positive definiteness, ensures computational efficiency, and provides a meaningful interpretation of the eigenstructure of the resulting mean tensor.
The advantages of the proposed approach are illustrated through an application to the Telecom Italia dataset, which collects mobile phone activity over a fine spatio-temporal grid. We focus on the metropolitan area of Milan, where the signal is strongly influenced by the proximity of highways and major roads which induce preferential spatial directions, together with daily and weekly cycles reflecting human mobility habits in the temporal dimension. By allowing for non-stationary anisotropic behavior, the proposed model provides a flexible and interpretable framework for analyzing these dynamics, producing quantitative insights that can support sustainability-oriented strategies such as the optimization of shared electric mobility services, improved traffic management, and a more efficient allocation of public resources.

Speaker: Ilenia Di Battista (MOX – Department of Mathematics, Politecnico di Milano)

12:15 Homogenization-Driven Modeling of Plant Tissue Dynamics

Hormonal activity, along with genetic regulation and vascular transport, plays a crucial role in regulating plant growth. In such mechanism, spatio-temporal signals are used to spread information across different portions of the plant. When multi-cellular tissues are involved in the transmission process, the evolution dynamics of such signals shows a multi-scale behavior. To model the information exchange, common mathematical approaches subdivide the considered tissue into multiple cellular domains where intra-cellular dynamics are accounted for by state variables that evolve according to ordinary differential equation models. However, this approach fails to retain spatial information at a sub-cellular level. Moreover, the numerical discretization of these models becomes demanding, especially in the case of high numbers of cells individually affecting different aspects of spatially-related phenomena (e.g., reaction and diffusion of chemicals).

To account for the spatial information while maintaining a manageable computational effort, we propose a new method that surrogates the effect of individual cell contributions on the macroscopic domain. To this aim, under the assumption that cells are arranged periodically within plant tissue, we treat a multi-scale problem through homogenization theory so that a coarse-grained averaged value of the individual cell contribution can be used as a good approximation of the real spatially heterogeneous coefficients.

The numerical test phase for the proposed approach is organized in multiple steps of increasing complexity. We start by considering a linear reaction-diffusion equation with different boundary conditions. Then, considering a variation, keeping the same coefficients as in the previous case, of the nonlinear Liouville-Bratu-Gelfand equation, for which analytical solutions are available in the literature, we validate the new model against a theoretical solution. Building on this, we extend the model to a system of coupled equations, and, finally, we apply the proposed approach to existing state-of-the art biochemical models.

Speaker: Nicolò Mondini

11:15 → 12:45 MS09+MS12 - Advances and Open Problems in CFD and FSI for Bioengineering Applications

11:15 Patient-Specific CFD versus Fluid–Structure Interaction Models of the Carotid Bifurcation

Atherosclerosis is a lipid-driven chronic inflammatory disease representing a leading cause of death globally, with plaques preferentially forming in regions of complex blood flow patterns, such as arterial bifurcations, bends, and branches. The role of local hemodynamics in atherosclerosis at the carotid bifurcation has been the subject of study by computational fluid dynamics (CFD) simulations for over three decades. However, the underlying assumption of rigid arterial walls is still a source of debate, with the growing interest around personalized, predictive in silico cardiovascular modelling. The complex interplay between blood flow and arterial wall mechanics can be modelled through fluid–structure interaction (FSI) approaches, nominally simulating more realistically the arterial biomechanical environment. However, its benefits must be carefully weighed against the increased computational cost, workload, and associated uncertainty.
In this study, ten subject-specific carotid bifurcations with ostensibly normal lumen geometries were analyzed using both rigid-wall CFD and two-way fully coupled FSI simulations. The FSI models incorporated an anisotropic fiber-reinforced hyperelastic arterial wall [1], estimation of the diastolic tensional state[2], viscoelastic support from surrounding tissue [3], and measurement-derived patient-specific inflow/outflow boundary conditions. Simulations were conducted using the monolithic finite-element based solver svFSI (SimVascular package [4]), based on the Arbitrary Lagrangian–Eulerian formulation (ALE) to model fluid-solid interaction. Qualitative and quantitative comparative analyses of wall shear stress-based metrics (including topological features) and intravascular flow patterns showed small to moderate differences between FSI and CFD simulations, suggesting that rigid-wall CFD simulations are generally sufficient to capture hemodynamic features of biological and clinical relevance. Nevertheless, the value of FSI for evaluating structural quantities that cannot be obtained through rigid-wall simulations, and for exploring their interaction with hemodynamic stresses on the endothelium, should not be overlooked.

[1]Holzapfel et al.,J Elast,2000
[2]Hsu et al.,Finite Elem Anal Des,2011
[3]Bäumler et al.,Biomech Model Mechanobiol,2020
[4]Zhu et al.,J Open Source Softw,2022

Speaker: Mariachiara Arminio (Politecnico di Torino)

11:30 Immersed Boundary Method for Mitral Valve Modelling

Mathematical and computational models of the heart offer insights into cardiac function that cannot be captured directly by medical imaging alone. Such models can inform patient-specific treatment planning, playing a central role in precision medicine. The mitral valve (MV) plays a important role in the cardiac function, regulating blood flow from the left atrium to the left ventricle. It is commonly impacted by pathologies such as prolapse, regurgitation and stenosis. In this talk, we first develop a fluid-structure interaction (FSI) model of the mitral valve that uses a physiologically realistic description of the MV leaflets and chordae tendineae. We implement this model in a validated immersed-boundary/finite-element framework, exploring the nodal coupling approach, which uses an identical set of points (the nodes of the structural mesh) for both the quadrature rule and Lagrangian interpolant, to obtain a diagonal mass matrix. In general, this requires 5-10 times fewer interaction points than the elemental approach used in previous work, improving the efficiency of simulations. However, leakage through the structure can occur when the structural mesh is relatively coarser than the background Eulerian grid. Results show that this approach is able to capture important characteristics of MV flow, such as vortices around the MV leaflets. Secondly, we explore a FSI model of a commercial phantom MV, that has been designed for learning and practicing leaflet repair. We match our structural mesh, boundary conditions, and the material properties of the leaflets and chordae to the experimental data, and show that our model is capable of reproducing results for leaflet closure, blood flow through the valve and fibre stress on the leaflets.

Speaker: Sarah Donaldson (University of Glasgow)

11:45 1-D CFD Model of Arterial Haemodynamics with Profunda Femoris Collateral Pathway: A Case Study in Lower-Limb Peripheral Artery Disease

Introduction: Computational fluid dynamics (CFD) models are widely used to study haemodynamics in the cardiovascular system. One-dimensional (1-D) CFD models provide an efficient framework for simulating pulse wave propagation in large arterial networks and generating in silico datasets for physiological analysis. In peripheral artery disease (PAD), arterial stenoses reduce blood supply to the lower limbs and may lead to critical limb ischaemia. Although 1-D CFD models have been applied to simulate arterial wave dynamics, many PAD simulations neglect key haemodynamic mechanisms, including energy dissipation across stenoses and the influence of collateral circulation. The profunda femoris collateral artery can provide alternative flow pathways that influence distal perfusion.

This study investigates the influence of collateral circulation and stenosis energy-loss modelling on haemodynamic predictions in a 1-D CFD model of the lower-limb arterial network.

Methods: An established 116-artery 1-D CFD model of the systemic circulation was extended to include the profunda femoris collateral pathway, resulting in a 130-artery representation of the lower-limb circulation. Stenoses of varying severity and configuration were introduced in the superficial femoral artery. Different stenosis energy-loss models were tested and incorporated in the arterial network. Pressure, flow rate, and perfusion distribution were compared between simulations with and without collateral pathways.

Results: Under healthy conditions, simulated pulse waveforms showed less than 1% root mean square error compared with the original 116-artery model and were consistent with reported physiological data. In PAD simulations, collateral pathways improved distal perfusion, particularly in severe and sequential stenoses. Critical stenosis thresholds for each PAD type were identified, and the role of collateral pathways was evaluated.

Conclusion: Collateral circulation and stenosis energy dissipation significantly influence haemodynamic predictions in PAD simulations. Incorporating these mechanisms improves the physiological realism of 1-D CFD arterial network models and supports the generation of physiologically consistent datasets for diagnostic modelling.

Speaker: Mia Wan (King's College London)

12:00 Predicting post-TEVAR endoleaks: a pre-operative hemodynamic risk factor from patient-specific Fluid-Structure Interaction simulations

Thoracic Endovascular Aortic Repair (TEVAR) is a minimally invasive procedure for the treatment of Thoracic Aorta (TA) pathologies, such as Thoracic Aortic Aneurysm (TAA). Computational simulations can provide valuable insights into TEVAR outcomes and complications (e.g., endoleaks) prior to surgery, making them a useful tool in the procedural planning. In this context, we develop a Fluid-Structure Interaction (FSI) computational framework to analyse the hemodynamics in different TAA scenarios. In this FSI model, blood is assumed to be Newtonian, homogeneous, and incompressible, and its behaviour is modelled with the Navier-Stokes equations written in the Arbitrary Lagrangian-Eulerian formulation. To account for transition to turbulence, particularly relevant in presence of TAA, the σ-model Large Eddy Simulation turbulence model is adopted. The aortic wall is assumed to be incompressible, and its dynamics is modelled using linear elasticity. The Young’s modulus of the healthy portion of the TA is set equal to 0.8 MPa, while for the aneurysmal region, a higher value of 1.2 MPa is imposed. For the fluid sub-problem, a physiological time-dependent pressure wave is imposed as inlet Boundary Condition (BC), an absorbing BC consisting of a single resistance is prescribed at each supraortics outlets, and a 3-element Windkessel model is applied at the descending TA outlet. For the structural sub-problem, on the external surface, a Robin BC is prescribed to model the constraint exerted by the surrounding tissue on the vessel’s movements. By means of this FSI model, we simulate the hemodynamics in ten pre-TEVAR patient-specific TAA scenarios, for which post-TEVAR outcomes (i.e., endoleak presence or absence) are known, to design a new hemodynamic risk factor able to predict post-TEVAR endoleaks. Then, we validate the risk factor prediction using post-TEVAR follow-up outcomes available for each patient-specific case. This is a first attempt to determine whether pre-TEVAR hemodynamics can effectively predict post-TEVAR complications.

Speaker: Francesca Duca (Labs - Dipartimento di Chimica, Materiali e Ingegneria Chimica - Politecnico di Milano, Milan, Italy)

12:15 Flexural Properties of Bone-Inspired Composite Structures Fabricated via Polyjet Technology

Bio-inspired composite architectures offer promising strategies to achieve a favourable trade-off between stiffness and energy absorption in engineered materials. Bone represents a paradigmatic example, where hierarchical organization and compliant–stiff interfaces contribute to complex deformation mechanisms under mechanical loading. In this work, the mechanical role of stiff interlayers (inspired by the cement line) and deformable cores was systematically investigated under flexural loading. Samples were fabricated using PolyJet multi-material 3D printing providing a controlled experimental platform. A set of layered and sandwich architectures was designed by combining glassy and rubber-like photopolymers with well-defined interfaces, enabling a rigorous analysis of the influence of interlayer position on flexural deformation modes considering both stiff and compliant matrices.
The results reveal that the placement of stiff interlayers strongly modulates the flexural response, highlighting a non-trivial interplay between layer position and bending-induced shear deformation. The introduction of a soft core significantly enhanced the energy absorbed at peak load compared to the single constituents, while preserving structural integrity. In particular, the best-performing configuration with a soft core absorbed approximately twice the energy absorbed by the monolithic samples built with the stiffest and strongest available material. Hybrid architectures combining interlayers and core–shell configurations further improved mechanical performance by promoting enhanced stress redistribution and deformation mechanisms.
Overall, this study provides design guidelines for layered composite architectures that balance stiffness and energy absorption through the combined effects of material contrast and interface placement, while offering insights into the potential mechanical implications of hard cement lines on the flexural behavior of trabecular bone.

Speaker: Matteo Sestini (Università di Pisa)

12:30 The Calliope Project and the Proposal of a Stress-Informed Approach for Upper-Limb Prosthesis Design

The development of next-generation upper-limb prostheses requires a patient-centered approach that prioritizes comfort, functionality, and anatomical integration. Traditional fabrication methods involve multiple manual steps and require the physical presence of the amputee. In contrast, advances in 3D printing now enable the production of lattice structures that provide an excellent balance of mechanical performance, combining stiffness, strength, and low weight. This study presents the design, numerical simulation, and additive manufacturing of an ultralight forearm socket based on lattice structures. Firstly, 3D scans of the residual limb, contralateral limb, and plaster model were acquired. Using the plaster scan, the liner was generated via offset and trimming along anatomical reference points. Two iterations corrected global alignment, and two further refined the anterior geometry. The outer socket was designed to restore anatomical proportions and accommodate myoelectric prosthetic components. A planar lattice structure was adopted for the socket, and polyamide 12 (PA12) was selected for manufacturing due to its mechanical properties, biocompatibility, and cost. Elastic-plastic homogenization was implemented to study the orthotropic behavior of lattice cells by varying strut diameters. Two test specimens with different lattice orientations were manufactured using multi-jet fusion (MJF) to validate the homogenized properties. Finally, finite element-based stress-informed optimization was used for the socket by adjusting strut diameters according to local stress, reinforcing high-stress areas and lightening low-stress zones. Comparison of stress–strain curves from homogenized, full-scale simulations and experiments showed excellent agreement. The optimized lattice reduced weight by 25.4% and 13.2% relative to solid and average-diameter lattice sockets, respectively with a minimum safety factor of 4.2. CT scans confirmed that the manufactured socket matched the CAD design. This methodology demonstrates a fully integrated workflow combining stress mapping, homogenization, and additive manufacturing to produce lightweight, anatomically compatible, and mechanically reliable prosthetic sockets, laying the foundation for future clinical investigations.

Speaker: Lorenzo Romanelli (University of Trento)

12:45 → 13:00 Group picture

13:00 → 14:00 Lunch break

14:00 → 16:00 MS02.1 - Advances in Neural Network Approximation and Surrogate Modeling for Scientific Machine Learning

14:00 NeuberNet: Leveraging Neural Operators for Elasto-Plastic PDE Solutions at Reentrant Corners via Low-Fidelity Elastic Inputs

Accurately simulating localized plastic strain at geometric discontinuities, such as reentrant corners, remains a significant hurdle due to the computational demands of fully nonlinear modeling. While simplified elastic methods are faster, they fail to account for critical nonlinear effects. To bridge this gap, we introduce NeuberNet, a Multi-Task Nonlinear Manifold Decoder designed to map far-field displacement data from coarse elastic simulations to high-fidelity stress and strain distributions.
The framework operates on axisymmetric solid mechanics principles, assuming bilinear isotropic hardening and small-scale plasticity. By applying the substructuring principle, NeuberNet restricts nonlinear computations to localized regions near stress concentrators, drastically improving efficiency.
Our study establishes specific mesh density requirements for input simulations and validates the model’s capacity to detect when small-scale plasticity limits are exceeded. Furthermore, we demonstrate NeuberNet’s versatility by applying it to 3D scenarios involving axisymmetric geometries under asymmetric loading. The results indicate that NeuberNet offers a robust, high-speed alternative for analyzing localized plastic deformation in engineering components.

Speaker: Tommaso Grossi (TeCIP Institute, Scuola Superiore Sant'Anna)

14:15 Accelerated inverse modeling of tumor evolution via Latent Dynamic Networks

The characterization of tumor evolution through partial differential equations (PDEs), ranging from reaction-diffusion systems to moving-interface models, provides essential insights into cancer progression. However, utilizing these high-dimensional frameworks in inverse settings to recover patient-specific biophysical properties is often computationally prohibitive due to the requirement for repeated forward evaluations.

We propose a novel framework for fast, grounded inversion by leveraging Latent Dynamics Networks (LDNets), introduced by Regazzoni et al. (2024), as consistent, causal surrogates. Rather than operating in high-dimensional discretized spaces, this architecture discovers a low-dimensional manifold to represent complex spatio-temporal dynamics. The architecture employs two neural components: $\mathcal{NN}_{dyn}$, which learns the intrinsic evolution of a latent state $s(t)$, and $\mathcal{NN}_{rec}$, a meshless reconstruction network mapping the latent state and spatial coordinates $x$ to the output field $\tilde{y}(x,t)$. This approach exploits the low intrinsic dimensionality of tumor growth dynamics. By leveraging the manifold hypothesis, we utilize the biophysiological regularity of tumor expansion as an inductive bias, allowing us to compress complex spatio-temporal evolution into a compact, low-dimensional latent space.

Because the surrogate is fully differentiable, it enables rapid parameter recovery even in non-ideal clinical scenarios. This includes inversion from noisy data or "non-rest" conditions where the initial state and timing of the tumor are unknown. Finally, the efficiency of this surrogate approach facilitates robust Uncertainty Quantification. By enabling rapid sampling methods, the framework provides a principled approach to estimating parameter posterior distributions, offering a more reliable foundation for predictive modeling in oncology

Speaker: Mikel Mendibe (University of the Basque Country / Tecnalia)

14:30 Data-Driven Resolution Enhancement of Electrostatic Potentials Using NextGenPB

Electrostatic interactions play a fundamental role in biomolecular recognition, binding affinity, conformational stability, and enzymatic activity. These effects are commonly modeled using the linearized Poisson–Boltzmann equation (LPBE), which provides a continuum description of electrostatics in implicit solvent environments. However, obtaining systematically converged high-resolution numerical solutions requires extremely fine spatial discretizations, resulting in substantial computational costs, particularly in multi-query and parametric settings.
In this work, we propose a neural surrogate framework for data-driven resolution enhancement of electrostatic potentials computed with NextGenPB. Rather than approximating the LPBE solution operator itself, we formulate the problem as the learning of a correction operator acting on coarse-grid numerical solutions. Given a coarse discretization of the LPBE solution, the neural network is trained to approximate the resolution-dependent correction that maps the coarse solution to its fine-grid counterpart on the molecular surface.
More precisely, the network learns a parametric representation of the discretization error, approximating the difference between fine- and coarse-grid solutions. The training process relies on analytically generated LPBE configurations, which provide exact reference solutions and ensure physics-consistent supervision. This construction allows the model to preserve the linear operator structure of the underlying equation while focusing on the approximation of resolution-induced discrepancies.
The surrogate is subsequently evaluated on realistic biomolecular geometries, where it provides a data-driven correction to coarse numerical solutions, enabling the recovery of refined electrostatic features without explicitly solving the LPBE on highly refined grids. This work contributes to the development of physically grounded neural surrogate models for PDE-based electrostatics, with emphasis on operator-consistent correction learning, cross-geometry transferability, and scalability in biomolecular simulation workflows.

Speaker: Vincenzo Di Florio (MOX Laboratory, Department of Mathematics, Politecnico di Milano, Piazza Leonardo Da Vinci, 32, Milano, 20133, Italy)

14:45 Dynamical reduced order approximation of Wasserstein gradient flows

This work introduces a novel dynamical reduced-order approximation framework for Wasserstein gradient flows that leverages the geometric structure of the solution manifold to construct an adaptive low-dimensional representation. The proposed method evolves the solution parametrization through appropriately designed systems of ordinary differential equations, allowing the approximation space itself to evolve in time, adapting to the underlying solution manifold. Such evolution is optimal with respect to the metric induced on the tangent space, ensuring an efficient and accurate representation of the system dynamics.

Wasserstein gradient flows arise in a wide range of applications spanning advection-diffusion PDEs and optimization, and their numerical treatment becomes particularly challenging in high-dimensional settings. In this regime, their approximation is challenged by the curse of dimensionality, the prohibitive cost of optimal transport computations, and sampling inefficiencies in the representation of evolving probability measures. These difficulties are compounded by nonlinear interactions and the simultaneous presence of diffusive and transport-dominated dynamics. In contrast, the proposed dynamical approach is mesh-free, achieves high accuracy with a small number of basis, and requires only a single sampling of the initial condition.

As a result, we provide a general nonlinear reduced-order model capable of accurately approximating a broad class of physical time-dependent phenomena, demonstraing ts effectiveness on several prototypical Wasserstein gradient flows.

Speaker: Isabella Carla Gonnella (SISSA)

15:00 Efficient Bayesian Inference for Uncertainty-Aware Scientific Machine Learning

Surrogate models such as PDE learners and machine learning force fields have become essential tools for approximating complex physical systems at a fraction of the computational cost of high-fidelity solvers. As these models are increasingly deployed in scientific and engineering workflows, quantifying their predictive uncertainty is critical for ensuring reliability and informing data acquisition strategies. Yet a persistent challenge remains: classical Bayesian inference methods, while principled, are often prohibitively expensive for the large-scale architectures that make modern surrogates so powerful. We present recent advances in Bayesian inference that treat computational efficiency as a first-class concern alongside trustworthiness and calibration. Our framework converts any surrogate model into an uncertainty-aware counterpart through a variational formulation that scales gracefully with model size and data volume, yielding calibrated uncertainty estimates without sacrificing the architectural flexibility that practitioners depend on. We further demonstrate how the framework naturally supports active learning, where predictive uncertainty drives adaptive sampling and experimental design, enabling more data-efficient construction of reliable surrogates.

Speaker: Dario Coscia (SISSA)

15:15 StabOp: A Data-Driven Stabilization Operator for Reduced Order Modeling

Spatial filtering has been widely used in under-resolved simulations of convection-dominated flows and, more recently, as a stabilization strategy in reduced order models (ROMs). However, spatial filters have key unresolved issues, such as determining the best-suited filter for specific applications or choosing an appropriate value for the filter radius.
To address these challenges, we introduce a fundamentally different approach that replaces traditional spatial filters with a data-driven stabilization operator (StabOp). The proposed StabOp is designed to deliver accurate results for a specified resolution, quantity of interest, and stabilization strategy. Although the framework applies to both classical discretizations and ROMs, as well as to various filter-based stabilization or closure techniques, we focus on ROMs with Leray stabilization.
To construct the StabOp, we assume a model form (linear, quadratic, or nonlinear) and determine its coefficients by solving a PDE-constrained optimization problem that minimizes a prescribed loss function. In the nonlinear case, the model is represented using a neural network, allowing for greater flexibility in capturing complex flow dynamics. Incorporating the learned operator into the Leray ROM (L-ROM) yields a new stabilized model, termed StabOp-L-ROM.
We evaluate the StabOp-L-ROM against the standard ROM and the classical L-ROM across four benchmark problems: 2D flow past a cylinder at Re = 500, lid-driven cavity flow at Re = 10000, 3D flow past a hemisphere at Re = 2200, and minimal channel flow at Re = 5000. The results demonstrate that, in predictive regimes, the StabOp-L-ROM can achieve accuracy improvements of several orders of magnitude over an optimally tuned L-ROM.

Speaker: Anna Ivagnes (SISSA)

15:30 Continuous Neural Network Approximations of Polygonal Basis Functions

We introduce two different neural-network-based strategies for the construction of conforming approximation spaces on general polygonal meshes for the numerical solution of partial differential equations. The proposed methodologies build upon the Virtual Element Method (VEM) paradigm, but replace the implicit definition of local basis functions with explicit neural representations.

In the original Neural Approximated Virtual Element Method (NAVEM), neural networks are trained to approximate the VEM basis functions on each element through a linear combination of harmonic functions. These learned representations are then employed within a standard finite element assembly. This strategy avoids the computation of problem-dependent VEM projection and stabilization operators, while preserving the geometric flexibility of polygonal discretizations. However, this original formulation generally produces basis functions that are exactly harmonic, as in the VEM framework, but discontinuous across element interfaces.

To overcome this issue, we develop two conforming neural variants, termed B-NAVEM and P-NAVEM, designed to enforce exact continuity of basis functions. Both approaches rely on fully connected feed-forward architectures but differ in their training principles.

The B-NAVEM formulation is based on a Physics-Informed Neural Network (PINN) with exact imposition of Dirichlet boundary conditions. This approach is employed to solve the local Laplace problems that define the virtual basis functions. The resulting functions are polynomial on element boundaries and approximately harmonic in the interior, thereby mimicking the structure of the VEM space while restoring conformity.

Conversely, rather than targeting the VEM space itself, P-NAVEM directly constructs continuous basis functions by training neural networks to enforce polynomial reproducibility, i.e., the key property that ensures optimal convergence rates.

Numerical experiments on linear and nonlinear model problems demonstrate that the proposed neural formulations achieve optimal convergence rates (up to neural-network accuracy) and exhibit competitive performance with respect to the standard VEM, while preserving its geometric flexibility.

Speaker: Gioana Teora (Politecnico di Torino)

15:45 Graph Neural Networks for Polytopal Mesh Agglomeration with Applications to Neurodegenerative Processes

Agglomeration techniques for polytopal meshes play a key role in reducing the computational cost of large-scale simulations, especially when high-order methods or complex geometries are involved. We introduce a geometrical deep learning framework for automatic mesh agglomeration, in which a Graph Neural Network learns to partition the connectivity graph of three-dimensional meshes and to construct agglomerated elements that meet stringent quality criteria. The model exploits both geometrical and physical information of the underlying domain, achieving fast online inference and enabling fully automated preprocessing pipelines. Numerical experiments on heterogeneous media and on complex three-dimensional geometries reconstructed from medical images show that the proposed approach yields agglomerated meshes with improved quality metrics and reduced runtimes compared to classical heuristic strategies.

This perspective naturally connects to advanced discretizations for partial differential equations on polygonal and polyhedral meshes. An application area in which these methods are particularly useful is the mathematical modeling of neurodegeneration. On the one hand, data-driven agglomeration enables accurate yet computationally affordable representations of intricate and heterogeneous brain structures, such as cortical folds or ventricular cavities. On the other hand, robust PDE solvers on polytopal meshes provide an efficient tool to describe the spatiotemporal evolution of pathological agents in neurodegenerative processes, where transport, nonlinear interactions, and tissue heterogeneity play a central role.

Speaker: Mattia Corti (MOX Laboratory, Department of Mathematics, Politecnico di Milano)

14:00 → 16:00 MS04.3 - High-Order Numerical Methods for Complex Mechanics and Higher-Order PDEs

14:00 A fast Poisson solver for isogeometric analysis

Consider the Poisson problem on a $d$-dimensional cube. It is well-known that, if the problem is discretized with linear finite elements on a uniform tensor product mesh, the resulting sti ness matrix can be diagonalized using the Fast Fourier Transform. This fact can be exploited to solve the linear system yielding $O(N \log N)$ complexity, where N represents the number of degrees of freedom. Such an approach is referred to as a fast Poisson solver. In this talk, we show how to generalize this idea to the case of B-splines of arbitrary degree $p$. The resulting algorithm solves the linear system with $O((N + p) \log N)$ complexity. This is achieved by splitting the spline space into an outlier-free subspace and a subspace with low dimension. On the latter subspace, the eigenvectors of the problem are computed numerically. On the former subspace, on the other hand, the eigenvectors are approximated using interpolated sinusoidal functions. The resulting approximated eigendecomposition can be used as a preconditioner for the linear system, yielding extremely fast convergence independently of $N$ and $p$.

Speaker: Mattia Tani

14:15 Stabilization-free Virtual Elements: the general order method

The Virtual Element Method (VEM) is a polygonal finite element method characterized by geometric flexibility and has therefore been applied to a wide range of engineering problems. Despite its popularity, some difficulties arise when dealing with strongly nonlinear and anisotropic problems, mainly due to the presence of a non-consistent stabilization term that needs to be introduced to ensure the well-posedness of the discrete problem.

Starting from the work in [1], in this talk we present the higher-order Stabilization-Free Virtual Element Method for general second order elliptic problems [2]. The proposed approach is based on a new polynomial projection that enables the construction of an operator-preserving scheme. Moreover, this new discretization allows the derivation of stabilization-free a posteriori error estimates, a result that cannot be achieved for the classical VEM on general polygonal meshes. The proposed framework opens new perspectives and applications also for higher-order problems, such as the biharmonic equation.

References

1. BERRONE, Stefano; BORIO, Andrea; MARCON, Francesca. A stabilization-free virtual element method based on divergence-free projections. Comput. Methods Appl. Mech. Engrg. 2024, vol. 424, Paper No. 116885, 19. issn 0045-7825, issn 1879-2138. Available from doi: 10.1016/j.cma.2024. 116885.

2. BERRONE, Stefano; BORIO, Andrea; FASSINO, Davide; MARCON, Francesca. Stabilization-free virtual element method for 2D second order elliptic equations. Comput. Methods Appl. Mech. Engrg. 2025, vol. 438, Paper No. 117839, 24. issn 0045-7825, issn 1879-2138. Available from doi: 10.1016/j.cma.2025.117839.

Speaker: Davide Fassino (Politecnico di Torino)

14:30 Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients

Virtual Elements (VEM) [1] generalize the Finite Element Method, allowing the discretization of complex geometries through general polytopal meshes.

The discrete space, which includes polynomials to ensure accuracy, is implicitly defined, as shape functions are solutions of a local PDE that is typically not solved. The discrete problem is constructed via polynomial projections, and well-posedness is ensured by a stabilization term accounting for the non-polynomial part of the space. However, the stabilization form is generally arbitrary and may not reflect the physical properties of the problem. Consequently, stabilization-free [2] or self-stabilized [3] VEM formulations are gaining popularity.

Moreover, an improper choice of polynomial projector and stabilization may deteriorate accuracy in the presence of variable coefficients.

This study [4] investigates the p-version of VEM and compares stabilized and self-stabilized formulations on academic benchmarks and application-oriented scenarios, particularly curvilinearly stiffened variable stiffness panels, widely used in aerospace structures.

References
[1] L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, A. Russo. Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(01), 199-214, 2013.
[2] S. Berrone, A. Borio, F. Marcon. Lowest order stabilization free virtual element method for the 2D Poisson equation. Computers & Mathematics with Applications, 177, 78-99 , 2025.
[3] A. Lamperti, M. Cremonesi, U. Perego, A. Russo, C. Lovadina. A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics. Computational Mechanics, 71(5), 935-955 , 2023.
[4] P. P. Foligno, D. Boffi, F. Credali, R. Vescovini. Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients arXiv preprint, arXiv:2511.18943, 2025. Computer Methods in Applied Mechanics and Engineering, to appear.

Speaker: Fabio Credali (King Abdullah University of Science and Technology)

14:45 Preconditioning the mass matrix for isogeometric immersed method

The mass matrix arising from the immersed isogeometric method is ill-conditioned due to the presence of severely trimmed elements in the computational domain, that is, elements of the mesh that only partially overlap with the domain of interest. We propose a preconditioning strategy based on the Additive Schwarz method.
Firstly, in contrast with existing methods, we use a preconditioner with Kronecker product structure rather than a simple diagonal scaling on the global space, to achieve a more robust preconditioner with respect to the polynomial degree. Secondly, we try a new approach for the construction of the Additive Schwarz local spaces, by considering basis functions with trimmed support, instead of trimmed elements. At the same time, since the local spaces associated to the trimmed degrees of freedom are more in number and larger than those related to trimmed elements, we investigate different strategies to select a subset of local spaces, with the aim of reducing the number of local spaces considered for the preconditioner, decreasing its computational cost, without affecting its performance.
Numerical experiments (in two dimensions) are considered to test the efficiency of the resulting preconditioners.

References:
[1] F. de Prenter, C. Verhoosel, G. van Zwieten, H. van Brummelen, ''Condition number analysis and preconditioning of the finite cell method'', Computer Methods in Applied Mechanics and Engineering 316 (2017).

[2] F. de Prenter, C. Verhoosel, H. van Brummelen, ''Preconditioning immersed isogeometric finite element methods with application to flow problems'', Computer Methods in Applied Mechanics and Engineering 348 (2019).

[3] G. Loli, G. Sangalli, M. Tani, ''Easy and efficient preconditioning of the isogeometric mass matrix'', Computers and Mathematics with Applications 116 (2022).

[4] F. de Prenter, C. Verhoosel, H. van Brummelen, M. Larson, S. Badia, ''Stability and conditioning of immersed finite element methods: analysis and remedies'', arXiv:2208.08538 (2022).

Speaker: Giovanni Varetto (Università Milano-Bicocca)

15:00 Anisotropic Refinement with Decoupled Patchwork B-Splines and Bézier Extraction

Classical THB-spline refinement in isogeometric analysis relies on nested tensor-product spaces, which limits its efficiency for strongly directional solution features. This work presents an anisotropic refinement framework based on decoupled patchwork B-splines (DPB-splines), enabling patch-wise and directionally selective refinement while preserving standard element-wise assembly. The construction couples patch-local basis functions with a recursive selection-and-truncation strategy and integrates Bézier extraction to flatten the hierarchy into standard element-level structures for straightforward assembly in existing finite element codes. The implementation is developed within the open-source GeoPDEs framework in Octave/MATLAB and is currently assessed on basic model problems designed to highlight directional refinement effects. These examples are intended to demonstrate feasibility, clarify the construction, and provide a foundation for more advanced anisotropic adaptive strategies in future applications.

Speaker: Andreas Grendas (TU Graz)

14:00 → 16:00 MS13.1 - Mechanics and Microstructural Behavior of Biological Media: from Multiscale Modeling to Simulations

14:00 Multiscale modeling of nematic films and incompressible poroelastic media

Multiscale systems are widely present in both biological structures and technological applications. The ability to account not only for the macroscopic behavior of an elastic medium, but also for its microscopic arrangement, allows for a more complete and realistic description. Recently, I studied two problems in which a non-trivial interaction
arises between two contributions coming from different scales of a structure.
In the first problem [1, 2], we prove the existence and geometric properties of an equilibrium configuration for a nematic film with surface tension using the Calculus of Variations. The key aspect is the non-trivial competition between the Frank energy of the crystal and the area functional.
In the second case [3], we derive the equations of Biot’s poroelasticity from the microstructure under the assumption of incompressibility of both an isotropic linear-elastic solid and a low-Reynolds-number Newtonian fluid flowing through its pores. By using the asymptotic homogenization technique, we obtain a macroscale system of PDEs, with corresponding cell problems at the pore-scale; moreover, we recover the equivalence between the change in volume of the porous solid and the volume of fluid exchanged.

References
[1] G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, A variational analysis of axisymmetric nematic films: the covariant derivative case, arXiv:2405.20154, Calculus of Variations and Partial Differential Equations, 2026.
[2] G. Bevilacqua, C. Lonati, L. Lussardi, A. Marzocchi, Existence and uniqueness of minimizers for axisymmetric nematic films, arXiv:2601.09348, submitted.
[3] R. Penta, C. Lonati, L. Miller, A. Marzocchi, Poroelasticity derived from the microstructure for intrinsically incompressible constituents, Zeitschrift f¨ur angewandte Mathematik und Physik, 2026.

Speaker: Chiara Lonati (Politecnico di Torino)

14:15 Modeling the biomechanics of the human iris with an active strain approach

The iris is a deformable circular diaphragm that regulates pupil size in response
to changes in illumination through the antagonistic actions of sphincter and
dilator muscles. While the phenomenological relationship between pupil size
and light intensity is well studied, the mechanical interplay between active
muscle contraction and passive iris tissue remains poorly understood. In this
study, we develop a finite element model of the human iris using an active strain
formulation to investigate the mechanics underlying pupil regulation under
physiological conditions. The iris is represented as a fiber-reinforced soft tissue,
with passive matrix behavior modeled as isotropic, nonlinear elastic and active
muscle contraction introduced via contractive strains along fiber directions.
Numerical simulations are performed using a dedicated finite element code. By
progressively including active and passive tissue components, we analyze how
tissue architecture affects pupil kinematics, stress distribution, and interaction
with supporting boundaries at the iris root. Results reveal a counterintuitive yet
significant role of passive tissues in shaping three-dimensional iris deformation
and moderating boundary reactions. This computational framework provides
a mechanically consistent basis for understanding iris biomechanics and can
support future studies extending to more complex physiological or pathological
conditions.

Speaker: Kevin Lucon (Politecnico di milano)

14:30 Modelling and simulation of anisotropic growth in brain tumours through poroelasticity: A study of ventricular compression and therapeutic protocols

Brain tumors remain one of the most formidable challenges in medicine, largely due to their unpredictable localization and varying degrees of malignancy. Their notorious aggressiveness in spreading often limits the efficacy of standard treatments. As the tumor mass grows, it compresses and displaces surrounding healthy tissues, often altering the volume of the cerebral ventricles and increasing intracranial pressure. Today, the standard of care typically relies on surgical resection, supplemented by radiotherapy and chemotherapy when needed.

To better understand and predict this behavior, this work introduces a multiphase mechanical model designed to simulate brain tumor growth. Specifically, our framework quantifies the solid deformations and stresses driven by tumor expansion. Crucially, the model incorporates the directionality of white matter fibers to capture the tumor's anisotropic growth patterns. By leveraging patient-specific Magnetic Resonance Imaging (MRI) and Diffusion Tensor Imaging (DTI) data, we are able to reconstruct highly realistic 3D brain geometries with precise ventricular representations. This allows us to deeply analyze how tumor growth mechanically impacts both the ventricles and the adjacent healthy tissue.

Through finite element simulations implemented in FEniCS, our numerical results highlight the model's accuracy in capturing the complex dynamics of tumor expansion and its mechanical consequences. Ultimately, the insights generated by this predictive framework hold significant potential to guide targeted, patient-specific therapeutic strategies, improving the overall clinical management of brain tumors.

Speaker: Francesca Ballatore (Université Côte d'Azur)

14:45 A micromechanical finite element model of the retina

In ocular biomechanics, the mechanical behaviour of the retina has received limited attention, as most studies have focused on the transduction of light into neuronal signals. Nevertheless, modelling retinal mechanics can provide valuable insights in the investigation of surgical procedures, such as subretinal injection, to evaluate the relevance of different surgical parameters on retinal rupture and detachment (L’Abbate, 2024). In this study, we propose a finite element model of the retina based on an innovative micromechanical approach, which focuses on the intrinsic discrete nature of the tissue seen as a network of structural elements and abandons more traditional continuum descriptions. The micromechanical model includes three layers: (i) a top network of trusses linking the top of the cells, modelling the internal limiting membrane, (ii) an intermediate layer consisting of vertical truss elements, representative of cells, such as cones, rods and Muller cells; and (iii) a bottom network of truss mimicking the bonds between cells at the interface with the retinal pigmented epithelium. The discrete geometry of the retina is generated with an ad hoc Matlab code, and numerical analyses are conducted with Abaqus. All structural elements are assumed to obey viscous-elastic constitutive laws. The elastic behaviours are modelled through Neo-Hookean materials, while the time-dependent behaviours through Prony series. The model has been used to simulate tensile and small punch laboratory tests on porcine retinas, revealing a better ability to capture the mechanical behaviour of the tissue with respect to alternative continuum models. Foreseen applications of the model include the simulation of the subretinal injection surgery, to assess the relevance of procedural variables such as injection rate, injection volume and absorption time on the retina.

Speaker: Damiano Bertolo (LaBS, Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano)

15:00 Multiscale continuous spectrum description of human fibrous tissues under dynamic conditions

Human fibrous tissues display a non-local in time mechanical behaviour since they have memory of their past stress-strain history and consequently they can be defined as hereditary materials. In particular, this unconventional behaviour can be mathematically described by introducing a fractional intermediate non-additive rheological model, the so-called springpot [1], to avoid the drawbacks linked to the use of the classical models in the description of hereditary materials with continuous retardation/relaxation spectra. However, the use of an intermediate model prevents the correct description of the real multiphase structure of hereditary materials and this has led to the emergence of drawbacks such as the impossibility to derive a unique formulation for the free energy function for the thermodynamical characterization of these materials.
In previous studies, in order to overcome all these drawbacks, a new multiscale hierarchical mechanically-based model was proposed to describe hereditary materials [2]. Indeed this model presents a complete separation of the fluid and the solid phases and, at the same time, is characterized, at limit, by a continuous relaxation spectrum. The main limitation associated to the use of this model is that it neglects the contribution of inertial forces in its mechanical description and consequently it cannot be used to describe biological tissues which are subjected to dynamic loading conditions where inertial effects significantly influence the material behaviour.
Consequently, the main aim of this study turns out to be the modification of this multiscale model to describe biological tissues under dynamic conditions.
Additionally, a numerical analysis is proposed to assess the goodness of the proposed approach.
[1] Nutting, P. G. 1921, “A new general law of deformation”, Journal of the Franklin Institute, vol. 191.5, pp. 679-685.
[2] Di Paola, M., Zingales, M. 2012, “Exact mechanical models of fractional hereditary materials”, Journal of Rheology, vol. 56.5, pp. 983-1004.

Speaker: Gaia Prezioso (Università degli studi di Palermo)

14:00 → 16:00 MS16 - Advanced FEM Techniques with Engineering Applications

14:00 (Cancelled) A Comparative Survey on Advanced Finite Element Methods for Solid Mechanics

The Finite Element Method (FEM) is one of the most powerful stretegies to solve boundary value problems in solid mechanics. It comes out, however, not without drawbacks, especially when dealing with complex geometries and discontinuities. Over time, several advanced FEMs have been developed to overcome the aforementioned limitations by eliminating or reducing the rigid reliance on the finite elements. These approaches include: (i) Meshless Methods (MMs), which represent the domain of a problem only by a set of arbitrarily distributed nodes; (ii) enriched Finite Element Methods (e-FEMs), which use any a priori knowledge of the solution to improve the finite element approximation space in a continuous Galerkin framework; (iii) the Virtual Element Method (VEM), which allows polytopal discretisation (polygons in 2-D or polyhedra in 3-D) of the geometry; (iv) Isogeometric Analysis (IGA), which exploits Non-Uniform Rational B-Splines (NURBS) as shape functions to blend FEM into CAD. To the best of the authors’ knowledge, a comparative survey of these FEM approaches seems to have drawn a limited attention. The aim of this study relies on an engineering perspective to the aforementioned advanced FEMs, comparing their accuracy and computational performance. Further, we discuss the advantages and disadvantages of the selected models through investigating their interplay with conventional FEM.

References
[1] Zienkiewicz O. C., Taylor R. L., Zhu J., (2005). "The Finite Element Method", Elsevier.
[2] Bathe K. -J., (1996). "Finite Element Procedures", Prentice-Hall.
[3] Liu W.K., Li S., Park H.S. (2022). "Eighty Years of the Finite Element Method: Birth, Evolution, and Future", Arch Computat Methods Eng 29, 4431–4453.

Speaker: Lucia Lottici (University of Pisa)

14:15 A VEM-Enhanced Immersed Interface Method for Moving-Boundary Problems on Fixed Grids

We introduce a numerical framework for moving-interface problems that integrates the Virtual Element Method (VEM) [1] within an immersed-boundary-type strategy [2,3]. In the proposed approach, the interface is represented in a Lagrangian manner and evolves within a fixed Eulerian finite element mesh. As the interface moves, it cuts the background structured grid, generating arbitrary polygonal subcells that are naturally handled as virtual elements.
Although a reconstruction of these polygonal regions is required at each update, achieved using standard computational-geometry procedures, this process avoids traditional mesh deformation, ensuring that elements never become distorted and eliminating the need for projection methods or sub-partitioning strategies [2,3]. The Eulerian–Lagrangian coupling enables accurate interface tracking while maintaining a stable and consistent solution of the governing equations on the fixed grid.
We demonstrate the effectiveness and versatility of the method in challenging scenarios involving tissue growth, third-medium contact, and erosion, all of which feature complex evolving geometries and large deformations. Numerical experiments show robust interface resolution and computational efficiency, highlighting the promise of this approach for multiphysics problems with moving boundaries.

References.
[1] P. Wriggers, F. Aldakheel, B. Hudobivnik. Virtual element methods in engineering sciences. Berlin: Springer, 2024.
[2] L. Foucard, A. Aryal, R. Duddu, F. Vernerey, 2015, A coupled Eulerian–Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries, Computer Methods in Applied Mechanics and Engineering, Volume 283, Pages 280-302.
[3] L. Kudela, N. Zander, T. Bog, S. Kollmannsberger, E. Rank, 2015, Efficient and accurate numerical quadrature for immersed boundary methods. Advanced Modeling and Simulation in Engineering Sciences, Volume 2, Pages 10(22).

Speaker: Alessandro Mastrofini (Multiscale and Multiphysics Mechanics Group (M2M), Department of Civil Engineering and Computer Science Engineering – University of Rome Tor Vergata)

14:30 VEM/BEM coupling for 3D acoustic scattering problems

Exterior problems in unbounded domains play a central role in the study of wave propagation, particularly in the modeling of scattering phenomena generated by obstacles represented by bounded regions. We focus on a three-dimensional exterior problem for the Helmholtz equation, endowed with Dirichlet boundary conditions on the surface of the obstacle and a suitable radiation condition at infinity.

To approximate its solution, we first introduce an artificial boundary enclosing the obstacle, thereby decomposing the exterior region into a bounded computational domain and an unbounded residual one. We then propose a numerical method based on the coupling of the Virtual Element Method (VEM) for the bounded interior domain (see [1]) with a Boundary Element Method (BEM) defined on the artificial boundary, following the Costabel–Han coupling strategy proposed in [2].

The VEM is by now a well-established and effective framework for problems posed in bounded domains, particularly well suited for handling complex geometries and general polyhedral meshes. Our aim is to extend its advantages to the treatment of unbounded domains through the proposed coupling approach.

To assess the performance and effectiveness of the method, we present a set of numerical experiments.

[1] L. Beirao da Veiga, F. Brezzi, L. Marini, G. Manzini, A. Cangiani, A. Russo (2013), Basic principles of Virtual Element Methods, Math. Models Methods Appl. Sci., 23, 199--214.
[2] G. N. Gatica, S. Meddahi (2020), Coupling of virtual element and boundary element methods for the solution of acoustic scattering problems, J. Numer. Math, 28, 223--245.

Speaker: Davide Collato (Politecnico di Torino)

14:45 (Cancelled) An Equivalent Temperature Load Approach for Creep and Shrinkage Consideration in the Ultimate Limit State Design of Reinforced Concrete Floor Slabs

Conventional design practice for reinforced concrete (RC) floor slabs employs linear elastic analysis, with nonlinear and time-dependent behaviors addressed through stiffness reduction factors applied post-analysis. Creep and shrinkage — two of the most significant time-dependent concrete properties — are conventionally accounted for at the Serviceability Limit State (SLS) through effective elastic modulus approaches, creep coefficients, and shrinkage curvature superposition. Leading design standards, including Eurocode 2, ACI 318M, and AASHTO LRFD, confine creep and shrinkage provisions predominantly to SLS verifications and stop short of providing clear provisions for their incorporation into Ultimate Limit State (ULS) design, leaving a notable gap in codified guidance. This gap is particularly consequential for large plan area RC floor slabs, where restrained shrinkage and creep-induced strains accumulate over extended lengths, generating internal stresses that can meaningfully alter moment and shear distributions at the ultimate limit state — consequently influencing reinforcement demand and its distribution across the slab.

To address this gap, a two-stage computational framework is proposed. In the first stage, nonlinear finite element analyses of suspended flat slabs are conducted in RAM Concept, explicitly modeling creep and shrinkage to establish reference internal stress and force resultant distributions. In the second stage, the same configurations are analyzed using linear elastic analysis, with creep and shrinkage represented as equivalent temperature loads incorporating internal restraint factors. Results from both stages are compared across a range of slab geometries and support conditions, spanning from full shear wall to column-only systems. From this comparison, a restraint factor R is calibrated such that the equivalent temperature load analysis reproduces the nonlinear moment and shear distributions to an acceptable degree of accuracy. The proposed factor R enables engineers to account for ULS implications of creep and shrinkage within a conventional linear elastic workflow, without recourse to computationally intensive nonlinear analysis.

Speaker: Pinel Getu Cherent (University of Pisa)

15:00 (Cancelled) Ultimate Buckling Strength Analysis of Cracked Stiffened Plates with Geometric Imperfections

A critical strength criterion for stiffened thin plates, such as ship hulls, is their ability to resist buckling. A ship is continuously supported by the buoyant volume of the hull, which changes under wave action and causes varying magnitudes of bending moment resisted by the longitudinally continuous structure within the hull girder. In the present work, a set of finite element analyzes (FEA) was carried out, using the commercial finite element package ANSYS APDL to reproduce the mechanical behavior of cracked stiffened panels when subjected to longitudinal compression. The objectives were to evaluate the buckling behavior and the stress-displacement relationship of the analyzed structures. The effect of crack size and the evolution of the stress intensity factor in three buckling analyzes were examined in this present work. Three positions of the stiffeners were considered and tested. Initial geometric imperfections based on a deformation mode were scaled and fed into physical and geometric incremental nonlinear analysis.

Speaker: Lahouaria Errouane (Laboratoire Structure De Composite et Matériaux innovants. Département de Génie Maritime, Faculté de Génie mécanique, BP 1505 El M’naouer, USTO, Oran, Algérie.)

15:15 A Bubble-Enriched Finite Element Method in a Fictitious Domain Framework for Dirichlet Problems

Many engineering applications, such as fluid–structure interaction and problems involving evolving domains, require efficient numerical methods for the solution of partial differential equations. In these contexts, the geometry of the domain may be complex or change over time. The fictitious domain method is a suitable tool for addressing this class of problems: the main idea is to embed the physical domain into a larger computational domain, where the mesh can be constructed more easily. This strategy avoids the need for boundary-fitted meshes and significantly reduces the complexity of the meshing process. A common strategy in fictitious domain formulations consists of imposing boundary conditions weakly by introducing suitable auxiliary variables supported on the embedded boundary. This approach leads to a mixed formulation, where the main challenge is to design discrete spaces that ensure a uniform inf–sup condition $[1]$. The presentation proposes a method for solving Dirichlet problems based on the introduction of local discrete spaces that satisfy this condition. We employ the use of element-level bubble functions, originally introduced to stabilize finite element computations. Depending on the position of the embedded boundary with respect to the mesh constructed on the larger domain, the finite element local spaces are enriched with two different types of bubble functions. Using a restriction operator as in $[2]$, this enrichment enables the proof of discrete inf–sup stability. Moreover, it allows to relax the requirement introduced in $[2]$ concerning the ratio between the boundary mesh-size and the domain mesh-size.
The presentation will also include classical error estimates and numerical results confirming the theoretical analysis.
$[1]$ Babuška, I (1973). The finite element method with Lagrangian multipliers, Numerische Mathematik, 20(3), 179-192.
$[2]$ Girault V., Glowinski R. (1995). Error analysis of a fictitious domain method applied to a Dirichlet problem, Japan Journal of Industrial and Applied Mathematics, 12(3), 487-514.

Speaker: Lorenzo Neva (Politecnico di Torino)

15:30 The position-based finite element formulation for structural nonlinear analysis and optimisation

The position-based finite element formulation (PFEF) assumes the nodal positions rather than the displacements as the primary unknowns. This formulation enables the derivation of simple analytical expressions of the secant and tangent stiffness matrices of isoparametric elements with any hyperelastic constitutive law [1].

Accordingly, the nonlinear governing equations are expressed as:

\begin{equation}
\mathbf{M} \ddot{\mathbf{x}} \left( t \right) + \mathbf{D} \dot{\mathbf{x}} \left( t \right) + \mathbf{S} \left[ \mathbf{x} \left( t \right) \right] \mathbf{x} \left( t \right) = \mathbf{p} \left( t \right) + \mathbf{r} \left( t \right),
\end{equation}
where $\mathbf{M}$, $\mathbf{D}$, and $\mathbf{S} \left(\mathbf{x}\right)$ are the global mass, damping, and secant stiffness matrices, respectively; $\mathbf{x}$ is the nodal position vector, $\mathbf{p}$ and $\mathbf{r}$ are the vectors of nodal loads and restraint reactions, respectively; an upper dot represents differentiation w.r.t. time, $t$.

The governing equations are solved by using an incremental-iterative arc-length method in statics and Newmark's method in dynamics.

In this talk, we present some examples concerning cable nets [2], wrinkling membranes [3], and curved rods [4]. Furthermore, we discuss the application of the PFEF for structural optimisation problems [5].

References
[1] Valvo PS (2025) Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity. Comput Mech 79:919-943. https://doi.org/10.1007/s00466-024-02539-4
[2] Fisicaro P, Pasini A, Valvo PS (2022) Simulation of Deployable Cable Nets for Active Debris Removal in Space. J Phys Conf Ser 2412:012010. https://doi.org/10.1088/1742-6596/2412/1/012010
[3] Valvo PS (2025) Position-based finite element formulation for the analysis of wrinkled membranes. In: Trovalusci P, Sadowski T, Ibrahimbegovic A (eds.) Multiscale and Multiphysics Modelling for Advanced and Sustainable Materials, Adv Struct Mater 231:417-429, Springer. https://doi.org/10.1007/978-3-031-84379-2_31
[4] Lottici L, Fisicaro P, Scheid SP, Valvo PS (submitted) A position-based formulation of the Hermite finite element for planar Kirchhoff rods: linear static and dynamic analysis. Comput Mech.
[5] Boyd S, Vandenberghe L (2004) Convex Optimization. Cambridge University Press. https://doi.org/10.1017/CBO9780511804441

Speaker: Paolo Fisicaro (University of Pisa)

15:45 An isogeometric collocation finite-strain visco-hyperelastic formulation for geometrically exact beams

We present a novel finite-strain mixed isogeometric collocation (IGA-C) formulation for the analysis of visco-hyperelastic geometrically exact beams. The model supports three-dimensional visco-hyperelastic materials while retaining the classical beam kinematic assumptions [1].
The three-dimensional constitutive equations are expressed starting from the stored energy function, which is split into an hyperelastic part and a dissipative part stemming for the viscous contribution. Adopting a linearized evolution law allows us to make use of a second-order accurate trapezoidal time-integration scheme, and to express rate-dependent parameters in terms of the one-dimensional geometrically exact beam
strain measures. This framework permits leveraging available SO(3)-consistent linearization approaches developed for finite-strain hyperelasticity [2].
The strong form of the governing equations is discretized using the IGA-C method, providing high spatial accuracy through smooth basis functions and avoiding element integrations. Furthermore, a mixed approach is used to mitigate locking effects. Numerical examples, including beams with complex initial curvature [3], demonstrate the capability of the model to reproduce large displacements and finite strains, including cross-sectional deformations.

REFERENCES
[1] S. Klinkel and S. Govindjee, “Using finite strain 3D-material models in beam and shell elements”, Engng. Comput, vol. 19, no. 3, pp. 254–271, 2002.
[2] D. Ignesti, G. Ferri, F. Auricchio, A. Reali, J. Kiendl, and E. Marino, “A novel finite-strain mixed isogeometric collocation formulation for hyperelastic geometrically exact beams”, Comput Methods Appl Mech Eng, 450, 118641, 2026.
[3] D. Ignesti, G. Ferri, F. Auricchio, A. Reali, and E. Marino, “An improved isogeometric collocation formulation for spatial multi-patch shear-deformable beams with arbitrary initial curvature”, Comput Methods Appl Mech Eng, 403, 115722, 2023.

Speaker: Diego Ignesti (Department of Civil and Environmental Engineering– University of Florence, Florence, Italy)

16:00 → 16:30 Coffee break

16:30 → 18:30 MS02.2 - Advances in Neural Network Approximation and Surrogate Modeling for Scientific Machine Learning

16:30 Deep Symmetric Autoencoders: Theoretical Framework and Practical Insights

Nowadays, autoencoders play a major role in reduced order modeling as they allow to represent the solution manifold of complex parameterized PDEs using few latent coordinates, thanks to their nonlinear nature. Indeed, their expressive power enables them to overcome the limitations of linear reduction methods, such as proper orthogonal decomposition (POD), which cannot break the so-called linear Kolmogorov barrier.

However, unlike linear reduction methods, generic autoencoders are not usually endowed with a rich mathematical structure providing a solid theoretical framework for their analysis and interpretation. In this respect, within this talk, we propose to study a class of constrained autoencoders which we refer to as deep symmetric autoencoders, which bridge the expressive power of neural networks and the well-established structure of linear methods. In doing so, we provide error estimates and, building upon them, we derive an initialization strategy. Our theoretical apparatus is then complemented by a set of numerical experiments providing practical insights on deep symmetric autoencoders.

[1] Brivio, S., & Franco, N. R. (2025). Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective. arXiv preprint arXiv:2506.11641.

[2] Otto, S. E., Macchio, G. R., & Rowley, C. W. (2023). Learning nonlinear projections for reduced-order modeling of dynamical systems using constrained autoencoders. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(11).

Speaker: Simone Brivio (MOX, Dipartimento di Matematica, Politecnico di Milano)

16:45 Multi-scale simulations of excitable cells through Finite-Basis PINNs

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving forward and inverse problems by embedding physical laws directly into the loss function. However, PINNs often struggle with spectral bias, making it difficult to capture the high-frequency oscillations and stiff dynamics present in modeling excitable cells. Finite-Basis PINNs (FBPINNs) address these limitations by integrating domain decomposition methods with deep learning. By partitioning the global domain into smaller subdomains, FBPINNs enhance the local approximation capabilities of the network, effectively capturing sharp gradients and fast temporal scales. In this work, we demonstrate the efficacy of FBPINNs in modeling excitable cells, which are governed by coupled reaction-diffusion partial differential equations with stiff ordinary differential equations. We focus on the FitzHugh-Nagumo model, a fundamental model in computational neuroscience and cardiology. Our results show how the FBPINNs can overcome the training instabilities of traditional PINNs when dealing with stiff ionic dynamics. Finally, we discuss the strengths and limitations of this approach.

Speaker: Luca Pellegrini (University of Pavia)

17:00 Bridging Numerical Methods and Neural Networks for PDEs

Partial Differential Equations (PDEs) play a central role in modeling complex phenomena arising in diverse applications, including battery life cycles, vegetation dynamics, renewable energy systems. Alongside classical numerical discretization techniques, recent advances increasingly rely on Neural Networks, particularly Physics-Informed Neural Networks (PINNs) [1], which approximate PDEs solutions in space and time by embedding the governing equations into the training process. This talk explores the interaction between standard numerical methods and neural network frameworks.

In the first part, we present new efficient W-methods for multidimensional PDEs, based on splitting and matrix-oriented strategies [2]. Their accuracy, stability, and computational efficiency are analyzed and compared. The effectiveness of these solvers is shown through the calibration of the two-dimensional Klausmeier vegetation model using satellite data, where convolutional neural networks are trained on datasets generated by repeatedly solving the PDEs system for varying parameters values.

In the second part, we show how classical time-integration schemes can be directly embedded within neural architectures, leading to discrete-time PINNs. In the approach we propose [3], the network outputs approximate the numerical solution at successive time steps. Numerical experiments indicate that the new PINNs are competitive with existing ones and offer an efficient framework for inverse problems such as parameters estimation.

References
[1] M. Raissi, P. Perdikaris, G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).
[2] D. Conte, S. González-Pinto, D. Hernández-Abreu, G. Pagano. On Approximate Matrix Factorization and TASE W-methods for the time integration of parabolic Partial Differential Equations. J. Sci. Comput., 100, 34 (2024).
[3] C. Valentino, G. Pagano, D. Conte, B. Paternoster, F. Colace, M. Casillo. Step-by-step time discrete Physics Informed Neural Networks with application to a sustainability PDE model. Math. Comput. Simul., 230, 541–558 (2025).

Speaker: Giovanni Pagano (Department of Agricultural Sciences, University of Naples Federico II, Italy)

17:15 Physics Informed Neural networks for downscaling on irregular meshes: successes and limitations

The DANTE project aims to create computationally efficient models of urban microclimate by applying model order reduction techniques to high-resolution urban-scale simulations. Resulting models must undergo a rigorous validation process before any application is possible, to ensure their accuracy and quantify their uncertainties. This validation process requires urban-scale ground truth data, which is not directly available. Instead, lower-resolution data must be downscaled to urban scale.

The lack of available data and models prevent the use of typical statistical and dynamical downscaling methods. Furthermore, the inhomogeneity of the scales of relevant flow structures requires that both input and target resolution data are irregular meshes, rather than grids. For these reasons, traditional downscaling methods are unsuitable. The goal of our work is to construct a downscaling framework adapted to the context of weather downscaling, leveraging regional model data, weather station measurements, and physical knowledge.

One solution is Physics-Informed Neural Networks (PINNs). PINNs incorporate physical constraints into the learning process by including PDE residuals into the loss function. By using a network that takes coordinates as input and outputs the local system state, a fitted model can be evaluated at arbitrary coordinates, providing a way to downscale (continuous PINN). However, a major downside of PINN is their lack of robustness: it can be difficult to get them to reliably converge.

In this context, we explore the difficulties that come from using PINNs, and ways around them. We define a criteria for PINN convergence based on the influence of the inclusion of physics in the loss, and study the influence on the PINN training process of architecture, collocation point density, weighting scheme of loss terms, preprocessing, and training protocol. We also present limitations of this method that we are not yet able to overcome, such as the dependency to initialization.

Speaker: Nemo Malhomme (Sant'Anna Pisa)

17:30 Leveraging neural active manifolds for stratified sampling

Propagating uncertainty from a potentially large number of random inputs through a computational model is becoming increasingly challenging due to the high cost of evaluating complex simulations. Stratified sampling is a well-known variance reduction strategy that, however, has mainly been employed in low-dimensional applications because of the difficulty of extending it to high-dimensional settings. In this talk, we propose using a recently introduced nonlinear dimensionality reduction approach, neural active manifolds (NeurAM), to enable stratified sampling in high dimensions. We leverage autoencoders to discover a one-dimensional manifold that captures most of the variability of the model output, aided by a simultaneously learned surrogate model whose inputs lie on this manifold. We then use the discovered neural active manifold to project a one-dimensional stratification back into the original input space, generating partitions that tend to follow the level sets of the model.

Speaker: Andrea Zanoni (Scuola Normale Superiore)

17:45 Generative A.I. meets Reduced-Order Modeling: partial knowledge and hidden parameters in physical systems

We introduce a new class of generative deep learning based reduced-order models (DL-ROMs) for uncertainty quantification and data-driven modeling of complex physical systems with hidden physics and/or partially observed parameters. Indeed, while DL-ROMs have been extensively shown capable of learning from numerical simulations, existing approaches are predominantly deterministic and assume full knowledge of the system, including physics and parameters. Although this is not problematic in traditional settings, we argue that some challenges naturally arise when trying to extend the idea to ROMs that can learn both from numerical simulations and real data. In fact, real-world phenomena typically deviate from simplified model-based simulations due to external uncertainties and an intrinsic lack of knowledge about the true nature of the system. To overcome these limitations, we develop probabilistic extensions of established DL-ROM architectures, including POD–NN and autoencoder-based models, designed to learn probability distributions over solution manifolds, thus capturing the additional variability induced by parametric uncertainty, model inadequacy, and noise in the observed data. In the same spirit of recent trends in the literature, our construction combines traditional DL-ROM architectures with ideas from generative AI,. We train our probabilistic ROMs using a variational loss, resulting in computationally efficient surrogates capable of producing multiple physically plausible solutions for any given value of the problem parameters. A rigorous theoretical analysis accompanies the methodological developments, addressing convergence of the learned distributions toward the laws of true solutions. The analysis relies on tools from empirical process theory, optimal transport, and approximation theory for deep neural networks. We demonstrate the proposed approach on stationary and time-dependent partial differential equations, including applications to flow in porous media and elastic deformation under uncertainty. The results show that generative probabilistic ROMs can offer a new interesting perspective, allowing us to reduce the gap between numerical simulations and real-world phenomena.

Speaker: Nicola Rares Franco (MOX, Dipartimento di Matematica, Politecnico di Milano)

18:00 A COMPARATIVE BENCHMARK OF FINITE VOLUME, REDUCED ORDER, AND PHYSICS-INFORMED SOLVERS FOR FLOW AROUND CYLINDER

Accurate simulation of unsteady fluid dynamics is critical for applications ranging from aerospace engineering to climate modelling. However, the prohibitive computational cost of high-fidelity solvers often precludes their use in real-time control. Traditionally, Finite Volume Method (FVM) solvers, such as Open FOAM, haveserved as the gold standard for accuracy but they are highly dependent on dense mesh discretization’s which creates a computational bottleneck. Reduced Order Models (ROMs) and Physics Informed Neural Networks (PINNs) have emerged as promising alternatives which acts as high-speed surrogates. In this work, we present a comparative analysis of FVM, POD-Galerkin ROMs, and PINNs applied to the canonical benchmark of unsteady flow around a cylinder at Re = 100. We demonstrate that the POD-Galer kin ROM technique reduces computational time forty-fold, slashing simulation du ration from 48 minutes to just 73 seconds, yet its utility remains strictly confined to the parametric range of the training snapshots. Conversely, we find that while PINNs offer mesh-agnostic flexibility, they often struggle to capture high-frequency vortex shedding due to spectral bias. Crucially, we show that augmenting PINNs with the ADAM-LFBGS optimizer effectively mitigates these stability issues, allowing them to match the fidelity of projection-based methods.

Speaker: Hassaan Idrees (IMT Lucca)

18:15 Machine Learning Surrogates for Robust Inverse Design of Shape-Morphing Elements

The inverse design of shape-morphing structures based on responsive polymeric materials, requires the development of theoretical and computational approaches capable of reproducing the involved physical phenomena. When gel-based morphing elements are considered, shape change capabilities can be easily obtained by harnessing their capability to react to external stimuli, such as humidity, temperature, PH variations, etc. These stimuli, if precisely spatio-temporally controlled, can be used to deform a structure from one configuration to another.
Recent advances in additive manufacturing enabled to easily obtain such systems; however, their design is often affected by multiple sources of uncertainty, including material properties, model inadequacy, and geometric errors.
In this work, we present an uncertainty-aware inverse design framework based on Machine Learning and probabilistic modelling for gel-based shape-morphing structures. The proposed approach integrates Approximate Bayesian Computation (ABC) to explicitly account for model-form and parameter uncertainties within the inverse design process. Neural network surrogates are trained to emulate the forward response of complex shape-morphing systems, including time-dependent deformation processes arising from swelling and diffusion phenomena. This enables the efficient incorporation of transient system dynamics within the Bayesian inference process.
As a representative application, a heterogeneous elastic tube embedding a swelling gel core is investigated, where swelling-induced forces drive shape change. The framework identifies spatial distributions of material properties required to match prescribed target shapes, while explicitly quantifying the impact of uncertainty and noise on the design outcome.
The results demonstrate that incorporating uncertainty significantly improves the robustness and reliability of ML-based inverse design, providing valuable insights for the development of shape-morphing systems with enhanced predictability.

Speaker: Silvia Monchetti (Università degli studi di Firenze - Dipartimento di Ingegneria Civile e Ambientale)

16:30 → 18:30 MS08 - Robust Preconditioning Techniques for Scientific Applications

16:30 A Mixed Precision Preconditioner for a Runge–Kutta Discretization of Instationary Incompressible Viscous Fluid Flow Problems

The flow of a Newtonian incompressible viscous fluid is a fundamental problem in computational sciences and engineering. In this case, the governing equations are the incompressible Navier–Stokes equations. For decades, researches have focused their interest on devising numerical methods for the solution of this problem. The non-linearity of the incompressible Navier–Stokes equations requires one to employ robust and efficient solvers for either the Picard or the Newton linearization of the discretized equations, which results in a sequence of linear systems to be solved in order to obtain a numerical solution. For instationary problems, the importance of a robust and efficient linear solver is even more evident, as at each time step one is required to solve a sequence of linear systems.

In this talk, we consider the numerical integration of the instationary incompressible Navier–Stokes equations, when employing a Runge–Kutta method in time. The time discretization results in a non-linear system to be solved for the stages of the Runge–Kutta method at each time step. In order to find a numerical solution, we employ a Newton linearization of the non-linear problem, which is then discretized with suitable finite elements. The resulting linear systems present a saddle-point block structure, and can be very large and sparse in real-life applications. For this reason, in order to find a solution one requires the use of preconditioned iterative methods. We employ an augmented Lagrangian strategy, and apply the preconditioner in mixed precision arithmetic. Numerical experiments show the effectiveness and robustness of our approach, together with the speed-up obtained in mixed precision arithmetic, for a range of problem parameters and different Runge–Kutta methods.

Speaker: Santolo Leveque (Charles University)

16:45 An algebraic-geometric multilevel preconditioner for continuous finite element discretizations

In this talk, we introduce a new hybrid approach for building geometrically informed algebraic multigrid preconditioners. Classical geometric multigrid methods are well known to be optimal preconditioners for linear systems arising from elliptic partial differential equations (PDEs). However, for very fine or complex geometries, the generation of a hierarchy might be not feasible. This issue is usually solved by employing algebraic multigrid (AMG) frameworks, which require only the system matrix to be given, without exploiting any geometrical information, but using matrix-entries only.

Our approach builds on a domain-decomposition setting. The core idea is to enrich the Nicolaides coarse space [1] with higher order basis functions, in order to extend AMG methodologies to high order elements. To this aim, we devise transfer operators defined through an efficient agglomeration algorithm based on the R-tree spatial data structures [2]. This coarsening strategy allows to inject geometrical information into the transfer operators, which are used as a tool to build coarser spaces.

We present a comprehensive set of numerical experiments, both in two and three dimensions on both structured and unstructured meshes, thereby confirming the effectiveness and efficiency of our approach as a multigrid preconditioner for continuous finite element discretizations.

[1] V. Dolean, P. Jolivet, F. Nataf. An Introduction to Domain Decomposition Methods: Algorithms, Theory and Parallel Implementation. SIAM, 2015

[2] M. Feder, A. Cangiani, L. Heltai. R3MG: R-tree based agglomeration of polytopal grids with applications to multilevel methods. Journal of Computational Physics, 526:113773, 2025

Speaker: Davide Polverino (Università di Pisa)

17:00 A non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology

Accurate, scalable numerical simulations are crucial for studying large-scale brain electrophysiology. We propose a massively parallel, two-level non-overlapping Schwarz preconditioner for the efficient solution of the algebraic systems arising from high-order polytopal Discontinuous Galerkin (PolyDG) discretizations of brain electrophysiology models. The study focuses on the monodomain equation coupled with the Barreto-Cressman ionic model, which describes the evolution of the transmembrane potential and ionic concentration dynamics in neural tissue. Spatial discretization is performed using high-order PolyDG methods on polytopal meshes, resulting in a large linear system to be solved at each time step. These systems are typically severely ill-conditioned, especially when polygonal meshes and high polynomial degrees are employed. To address this issue, we design an additive Schwarz preconditioner based on a non-overlapping domain decomposition with an agglomerated coarse space. The approach combines independent local subdomain solvers with a global coarse correction.

Numerical experiments on sequences of nested polytopal meshes, modeling heterogeneous grey and white matter tissues, assess robustness with respect to mesh refinement, polynomial degree, and coarse-to-fine mesh ratios. The results show that the proposed preconditioner significantly lowers condition numbers and iteration counts compared to the unpreconditioned solver, while maintaining scalability for fixed coarse-to-fine ratios.

Speaker: Caterina B. Leimer Saglio

17:15 Transforming smoothers for elliptic interface problems

We consider the fictitious domain formulation for elliptic interface problems introduced in [1]. The linear system arising from the mixed finite element discretization exhibits a double saddle-point structure, which makes it challenging to solve.
In this talk, we discuss the application of transforming smoothers [2] as an effective preconditioning technique.

References
[1] D. Boffi, L. Gastaldi, M. Ruggeri. Mixed formulation for interface problems with distributed Lagrange multiplier. Computers & Mathematics with Applications 68.12 (2014): 2151-2166.
[2] G. Wittum. Multi-grid methods for Stokes and Navier-Stokes equations: Transforming smoothers: Algorithms and numerical results. Numerische Mathematik 54.5 (1989): 543-563.

Speaker: Fabio Credali (King Abdullah University of Science and Technology)

17:30 Efficient solution of discontinuous Galerkin approximation of the non-linear thermo-poroelastic problem

The efficient and accurate simulation of coupled multi-physics phenomena is a fundamental challenge in various scientific and engineering disciplines. Such problems, which involve the interplay of multiple physical processes, often result in large and potentially ill-conditioned linear systems. The computational demand associated with solving these systems can be prohibitively high. As a consequence, researchers and practitioners have sought innovative solution strategies to address these computational challenges. In this work, we inspect the efficient solution of the four-field formulation of the non-linear thermo-poroelastic problem. The study includes preliminary results and theoretical findings on different strategies for addressing the solution of large ill-conditioned linear system. For the spatial discretization, we design a high-order symmetric weighted interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. When designing the solution strategy, a particular focus is devoted to the treatment of the non-linear convective transport term in the energy conservation equation proposing suitable stabilization techniques that make the scheme robust for advection-dominated regimes and trying to exploit the solution strategy for reducing the complexity of the problem. A broad set of numerical simulations is presented to validate the theoretical analysis, to inspect numerically the robustness properties, and to test the capability of the proposed method in a practical scenario inspired by a geothermal problem.

Speaker: Stefano Bonetti (stefano.bonetti@polimi.it)

17:45 Efficient and Stable Dirichlet–Neumann Methods for Fluid–Structure Interaction with Large Added Mass

Solving fluid-structure interaction problems when the fluid and structure densities are similar (large added mass), as in hemodynamics, is challenging because the stability and convergence properties of the adopted numerical scheme can be compromised. This is especially true for partitioned schemes, whose modularity is otherwise attractive, since it allows exploiting the favorable numerical properties of the sub-problems, which are better conditioned (than the monolithic one), and possibly existing standalone fluid and structural codes. In this regard, the classical Dirichlet–Neumann (DN) coupling scheme, which provides the most natural partitioned formulation of the fluid and structural subproblems, is known to suffer from severe convergence and stability issues in large added-mass regimes.
In this work, we revisit DN coupling from an algebraic viewpoint. Building on its interpretation as a Richardson iteration equipped with a block Gauss–Seidel preconditioner and acceleration parameter α = 1, we design improved coupling strategies suited for large added-mass regimes by considering optimal values of α. We discuss both strongly coupled and loosely coupled formulations, which can be interpreted as preconditioned solvers for the interface problem, and analyze their convergence and stability properties in the presence of large added-mass effects. We further explore strategies to enhance the robustness and practical applicability of these methods. In particular, we investigate automated procedures for selecting stable values of the parameter α, including machine-learning-based approaches, and we study correction strategies to improve the temporal accuracy of the loosely-coupled schemes.
Numerical experiments in hemodynamic settings illustrate the behavior of the proposed methods and highlight their potential as robust preconditioning strategies for coupled multiphysics problems

Acknowledgments
The authors acknowledge their membership in INdAM GNCS.
The authors have been partially supported by the European Union-Next Generation EU, Mission 4, Component 1, CUP: D53D23018770001, research project MIUR PRIN22-PNRR n.P20223KSS2.

Speaker: Francesca Renzi (Politecnico di Milano)

16:30 → 18:30 MS13.2 - Mechanics and Microstructural Behavior of Biological Media: from Multiscale Modeling to Simulations

16:30 Variational methods and internal constraints in poroelastic theories

We investigate the growth and remodeling of biological tissues, described as multi-constituent materials, and the structural evolution associated with these phenomena. We generalize the results obtained in [1, 2], and we frame them within the context of the Analytical Mechanics of nonholonomic systems. We do this to study growth variationally.

Inspired by [3, 4], we start from a multiplicative decomposition of the deformation gradient tensor in which the factor associated with the growth-induced distortions evolves according to prescribed “growth laws” [3, 4]. Without suitable assumptions, the resulting constraints are nonholonomic. By appending such constraints to a proper Lagrangian density function, we derive the dynamic equations through the extended Hamilton-Suslov Principle, and we show that they agree with those obtained by exploiting the Principle of Virtual Work.

References
[1] Grillo, A., Federico, S., Wittum, G., “Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials”, Int. J. Non-Linear Mech., 47, 388–401 (2012).
[2] Licari, V., “Considerazioni sulla possibilità di formulare alcune leggi evolutive della crescita volumetrica di aggregati cellulari ”, Tesi di Laurea Magistrale in Ingegneria Matematica, Politecnico di Torino, (2021).
[3] Grillo, A., Pastore, A. and Di Stefano, S., “An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems”, J. Elast., 157, 388–401 (2024).
[4] Pastore, A., Giammarini, A., Grillo, A., “Reconciling Kozlov’s vakonomic method with the traditional non-holonomic method: solution of two benchmark problems”, Acta Mech., 235, 2341–2379 (2024).

Speaker: Francesco Turiano (Politecnico di Torino)

16:45 Dynamic instability of a charged Ziegler's double pendulum.

The exploitation of instabilities within solids and structures has gained a lot of attention in recent years [1], with instabilities now being embraced in design rather than avoided. One potential application arises for micro-robotics within biological environments, where dynamic instabilities can be used to generate motion [2, 3].

This presentation investigates the possibility of exploiting the dynamic instabilities of a constrained version of Ziegler’s double pendulum, as imagined by Cazzoli et al. [4, 5], for micro-robotic applications. As shown in [6], a charge is introduced at the tip of the double pendulum, and the system is placed within, or in the proximity of, an ideal solenoid. The resulting interaction with the magnetic field is examined, to determine how electromagnetic effects influence the overall dynamics and whether they may provide a mechanism for controlling the motion of the device.

Acknowledgements: Financial support from ERC-ADG-2021-101052956-BEYOND

References
[1] Kochmann, D. M., Bertoldi, K., “Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions”, Applied Mechanics Reviews, 69, 050801 (2017).
[2] Zhu, L., Stone, H. A., “Propulsion driven by self-oscillation via an electrohydrodynamic instability”, arXiv preprint, arXiv:1906.03076, (2019).
[3] Boiardi, A. S., Noselli, G., “Minimal actuation and control of a soft hydrogel swimmer from flutter instability”, J. Mech. Phys. Solids, 191, 105753, (2024).
[4] H. Ziegler, Principles of Structural Stability, Lehr- und Handbücher der Ingenieurwissenschaften, Birkhäuser Basel, (1977).
[5] Cazzolli, A., Dal Corso, F., Bigoni, D., “Non-holonomic constraints inducing flutter instability in structures under conservative loadings”, J. Mech. Phys. Solids, 138, 103919 (2020).
[6] Pastore, A., Harrop, J.C., Bigoni, D., Grillo, A., “Dynamics of a charged Ziegler’s double pendulum under the joint action of a follower force and Lorentz force”, (2026) Submitted.

Speaker: Joel Harrop (University of Trento)

17:00 The functional impact of myofiber macroscopic organization and disarray in computational models of the murine heart

A major challenge in computational models of cardiac electromechanics is the reconstruction of myocardial fiber architecture, as direct in vivo measurements of fiber orientation are not feasible. Consequently, rule-based methods are commonly adopted as surrogates, relying on empirical descriptions of fiber organization combined with patient-specific geometries. This study investigates the respective roles of macroscopic fiber architecture and microscopic fiber disarray in cardiac electromechanical simulations. A high-fidelity biventricular electromechanical model of a murine heart was developed using a high-resolution myocardial fiber field obtained via Mesoscopic Optical Imaging (MOI), which serves as a reference ground truth. A spatial smoothing strategy is introduced to decouple macroscopic fiber organization from local disarray, and the resulting responses are also compared with those obtained using a rule-based fiber field. The results show that passive mechanics and electrophysiological activation are only weakly affected by fiber disarray. In contrast, active mechanics is highly sensitive to fiber architecture. Moderate regularization of the experimentally measured fiber field enhances the ventricular pumping efficiency of the computational model by reducing microscopic disarray while preserving the macroscopic helical organization, whereas excessive smoothing or rule-based fiber reconstructions lead to unphysiologically strong or inefficient contraction. Within this framework, two commonly adopted surrogate strategies to account for fiber disarray are investigated: (i) a reduction of the effective cross-bridge stiffness in the active tension model, and (ii) the introduction of controlled misalignment between active tension and the local fiber direction. While
both approaches reproduce global hemodynamic indicators comparable to the reference case, an effective reduction of contractility – despite its phenomenological nature – provides a closer match to the reference
strain patterns than the introduction of orthogonal active stress components. Overall, the results highlight the dominant role of macroscopic fiber architecture in active mechanics and reveal important limitations of commonly adopted surrogate approaches for modeling fiber disarray.

Speaker: Carlo Guastamacchia (Politecnico di Milano, DMAT, MOX lab)

17:15 The mechanics of active fiber-reinforced plates: modeling curvature-induced cell alignment

Biological tissues frequently feature complex internal architectures, such as fiber networks, that strictly govern their mechanical behavior. Although the continuum mechanics of isotropic thin bodies incorporating biological effects, such as morphogenesis and internal activity, is well established $[1,2]$, a unified framework capturing anisotropy remains lacking.
This talk presents a rigorous continuum theory for active, anisotropic inelastic plates. By employing a multiplicative decomposition of the deformation gradient alongside fiber-dependent constitutive laws, we integrate incompatible active deformations with structural directionality. Through an asymptotic expansion of the three-dimensional energy functional under suitable scaling, we derive an effective plate theory within the Föppl–von Kármán regime. The resulting system of PDEs transparently captures the mathematical interplay between geometry, activity, and anisotropy $[3]$.
We apply this limit theory to investigate curvature-induced cell alignment. Modeling a cell as a fiber-reinforced active plate, we reveal that the system's response is governed by a dimensionless ratio comparing internal activity to substrate curvature. This ratio drives a bifurcation predicting a non-trivial range of optimal fiber orientations. Offering qualitative agreement with experimental observations, this framework is able to capture the essential mechanics of active, anisotropic thin biological structures.

References

$[1]$ J. Dervaux, P. Ciarletta, and M. Ben Amar. “Morphogenesis of thin hyperelastic plates: a constitutive theory of biological growth in the Föppl–von Kármán. Journal of the Mechanics and Physics of Solids 57.3 (2009), pp. 458–471.

$[2]$ L. A. Mihai and A. Goriely. “A plate theory for nematic liquid crystalline solids”. In:Journal of the Mechanics and Physics of Solids 144 (2020), p. 104101.

$[3]$ G. Fioretto et al. “The mechanics of anisotropic active plates with applications to cell alignment on curved substrates”. In: arXiv preprint arXiv:2512.19755 (2025), (under review)

Speaker: Gabriele Fioretto (Politecnico di Torino)

17:30 Data-driven Discovery of Convex Dissipation Potentials in Viscoelasticity via Grammar-Based Symbolic Regression

We propose a thermodynamically consistent, physics-informed symbolic-regression framework for the automated discovery of convex dual dissipation potentials in viscoelasticity. Within the generalized standard materials (GSM), we characterize internal-variable dynamics through a gradient flow $\dot z = (\varphi^{*})'(A)$ driven by the thermodynamic force $A = \partial \psi / \partial z$. By embedding convexity as a structural constraint directly into the hypothesis space, the framework identifies parsimonious, explicit expressions for $\varphi^{*}$ that rigorously satisfy the Clausius–Duhem inequality and ensure the well-posedness of the evolution equations.

A convexity-preserving formal grammar restricts the hypothesis space to thermodynamically admissible potentials via production rules enforcing closure under positive linear combinations and utilizing convex primitives. Function composition is strictly regulated to maintain convexity as an invariant property across the expression tree. To navigate this constrained landscape, we employ a genetic programming (GP) algorithm with an embedded nonlinear parameter-optimization stage, calibrating coefficients by minimizing stress reconstruction discrepancy during the temporal rollout of the internal-variable evolution.

Framework robustness is evaluated using "virtual DMA'' datasets from a one-dimensional generalized Maxwell solid across various strain amplitudes and frequencies, incorporating Gaussian noise and temporally correlated (Ornstein-Uhlenbeck) perturbations. For a Newtonian-viscosity ground truth, the algorithm consistently recovers the exact quadratic structure with negligible error. In nonlinear power-law cases, the identified functional form matches the underlying behavior across nearly all stochastic realizations. Validation against experimental DMA measurements further confirms that the discovered potentials accurately capture storage and loss moduli across diverse loading regimes.

Ultimately, this convexity-preserving symbolic framework establishes a robust, interpretable, and physics-consistent pipeline for the data-driven identification of dissipative mechanisms, offering a transparent alternative to black-box models for the constitutive characterization of complex materials and soft biological tissues.

Speaker: Federico Califano (Sapienza University of Rome)

16:30 → 18:30 MS15 - Theoretical and Computational Mechanics of Time-Dependent Materials

16:30 Unsteady incompressible flow of a dispersive transversely isotropic material in a planar channel

In this work, we consider a linearized model for transversely isotropic bodies, in which dispersion is characterized by a preferred direction. We investigate the unsteady incompressible flow of these materials in a planar channel under suitable boundary and initial conditions. The problem is reduced to a system of time-dependent partial differential equations, which is solved using projection algorithm based on spectral methods. We quantify how anisotropic dispersion and material stiffness affect the displacement field.

Speaker: Rebecca Tozzi (Università di Firenze)

16:45 Analysis of the D.C.B. test via damage phase-field modeling

Adhesive bonding technology is increasingly being adopted in the automotive, aerospace, and
naval sectors [1], driven by the demand for lightweight and easy-to-assemble joints, as well as
by advances in chemical formulations. Its application in safety-critical components poses sig-
nificant modeling challenges, requiring an accurate representation of both in-service behavior
and failure mechanisms.
To reproduce and generalize the mechanical behavior of these joints, a phase-field damage
model is proposed. Three different modeling approaches are considered:
1. a 2D plane-strain model;
2. a hybrid 1D–2D model, in which the bonded substrates are modeled using Timoshenko–Ehrenfest
beam elements, while the adhesive layer is represented by a 2D plane-strain shell;
3. a purely 1D model, where the adhesive (mastic) is described through a dedicated 1D
formulation.
The first two approaches allow for the analysis of the volumetric behavior of the joint under
various conditions (e.g., different adhesive thicknesses and plane stress/plane strain loading
states). Furthermore, they can be employed to identify the parameters required for the 1D
model. However, these approaches are computationally demanding and therefore not well suited
for large-scale simulations.
The purely 1D model, while unable to capture the full volumetric behavior and all the spe-
cific effects addressed by the higher-dimensional approaches, is computationally efficient and
straightforward to implement, making it suitable for large-scale analyses.
All these approaches preserve the flexibility of the phase-field framework, which can be further
enriched by incorporating finite elasticity models and finite viscoelasticity (e.g., [2]).
REFERENCES
[1] O. Sapronov et al, Development and use of new polymer adhesives for the restoration of
marine equipment units. Journal of Marine Science and Engineering (2020) 8(7), 527.
[2] Ciambella, J., Lancioni, G., Stortini, N. (2025). A finite viscoelastic phase-field model
for prediction of crack propagation speed in elastomers. European Journal of Mechanics-
A/Solids, 113, 105678.

Speaker: Nico Stortini (ENSTA Bretagne)

17:00 An approach to nematic elastomers based on extended constraints

Nematic elastomers are cross-linked polymer networks where rod-like mesogens, described by a director field, determine the material’s internal structure. Standard theories in soft elasticity assume macroscopic isochoricity (incompressibility) and the mesogens’ inextensibility. These conditions can be enforced as internal constraints, thereby aligning with thermodynamically compatible frameworks [1, 2]. Yet, inspired by recent investigations [3], we addressed in [4] the possibility of “extending” the inextensibility condition to hold explicitly also on the boundary of the elastomer via an appropriate boundary Lagrange multiplier. In this presentation, we report the main outcomes of our study, which involve potential computational advantages, alternative interpretations of known stability results, and the use of gauge relations in nematic elastomers.

References
[1] Anderson, D.R., Carlson, D.E., Fried, E., “A continuum-mechanical theory for nematic elastomers”, J. Elast. 56, 33–58 (1999).
[2] Chen, Y., Fried, E., “Uniaxial nematic elastomers: constitutive framework and a simple application”, Proc. R. Soc. Lond. A 462, 1295–1314 (2006).
[3] Steigmann, D.J.: Lagrange multipliers at the boundary in the inextensional bending theory of thin elastic shells. Math. Mech. Solids 30(2), 211–217 (2023).
[4] Pastore, A., Grillo, A., Fried, E., “Internal constraints and gauge relations in the theory of uniaxial nematic elastomers”, Journal of Elasticity, 158, 10 (2026).

Speaker: Andrea Pastore (Politecnico di Torino)

17:15 Extensional–torsional coupling in spider silk under different environmental conditions

Environmental conditions strongly influence the mechanical response of spider silk and therefore must be considered when interpreting experiments and designing silk-inspired materials [1, 2, 3]. In particular, variations in relative humidity can induce supercontraction together with a concomitant torsional response. However, these coupled effects have not yet been systematically investigated from either an experimental or a theoretical perspective. In particular, a macromolecular-scale interpretation of humidity-driven twist, and of its interaction with loading history, is still lacking. Here, we perform experiments under controlled environmental conditions to quantify the coupled evolution of axial deformation and torsion during humidity-driven supercontraction and mechanical loading. We then interpret the experimental results through a micromechanics-based model, inspired by the dual Poynting effect in fiber-reinforced cylinders [4], to relate humidity-induced axial shortening to the observed torsional response. In addition, cyclic tests reveal the onset of residual strain and its concomitant influence on torsion, indicating that loading history can alter the subsequent twist evolution during humidity cycles. The modeling framework is therefore extended to capture the coupling between residual deformation and torsional response. Overall, the combined experimental evidence and modeling provide a unified picture of how environment and loading history jointly govern spider-silk mechanics, and offer transferable tools for hygroscopically active fibers and bioinspired actuators.
References
[1] V. Fazio, D. De Tommasi, N. M. Pugno, G. Puglisi, J. Mech. Phys. Solids 164, 104857 (2022).
[2] V. Fazio, N. M. Pugno, G. Puglisi, Extreme Mech. Lett. 61, 102010 (2023).
[3] V. Fazio, A. D. Malay, K. Numata, N. M. Pugno, G. Puglisi, Adv. Funct. Mater. 35, 2420095 (2024).
[4] M. Fraldi, G. Puglisi, G. Saccomandi, Proc. R. Soc. A 481, 20240816 (2025).

Speaker: Vincenzo Fazio (University of Trento)

17:30 A poroelastic approach in modelling the corneal keratoconus

The keratoconus is a pathological condition that can affect the shape of the human cornea, which is the dome-like, hydrated, transparent tissue with structural function that withstands the pressure exerted by the physiological intraocular pressure [1], and causes it to assume a conical shape. Albeit the biological causes for the insurgence of keratoconus are currently unknown, several studies [2] suggested to interpret it as a localized reduction in the mechanical properties of the tissue, which can be regarded as a multi-constituent material, composed of keratocytes, collagen fibers and extracellular matrix.

In our work, we include a description of the behavior of the fluid, thus studying the healthy corneal tissue as a saturated poroelastic medium that undergoes large deformations due to the intraocular pressure exerted by the aqueous humor [3,4]. This serves as a baseline for introducing the degradation of the mechanical properties of the solid phase, which is accompanied by an alteration in the hydraulic properties of the medium. We perform finite element numerical simulations with physiological and pathological parameters, and show that our biphasic model is able to capture qualitatively and quantitatively the alteration of cornea’s shape and the reduction of thickness [5]. In particular, in the keratoconus cases we obtain a reduction of the thickness up to 40% of the healthy ones.

References
[1] Meek K. M. et al. Current Eye Research, Vol. 6, No. 7, Informa UK Limited, p. 841-846 (1987).
[2] Pandolfi, A., De Bellis, M. L., Mechanics of Materials, Vol. 199, Elsevier BV (2024).
[3] Hassanizadeh S. M., Advances in Water Resources, Vol. 9, p. 207-222 (1986).
[4] Giammarini, A., Pandolfi, A., Mechanics of Materials, Vol. 214, Elsevier BV (2026).
[5] Rabinowitz Y. S., Survey of Ophthalmology, Vol. 42, No. 4, Elsevier BV, p. 297-319 (1998).

Speaker: Alessandro Giammarini (Politecnico di Milano)

17:45 Variational Formulations for Viscoelasticity with Anisotropic Evolution of Viscous Strain

Biological tissues are intrinsically viscoelastic and highly anisotropic, owing to the complex spatial distribution of embedded fibres, predominantly collagen. Accurately modeling these time-dependent, directionally biased mechanical responses under large deformations remains a cornerstone of theoretical biomechanics and holds significant diagnostic potential for biomedical applications.

To this end, we propose a theoretical and computational framework for anisotropic finite-strain viscoelasticity. The model relies on the multiplicative decomposition of the deformation gradient combined with an additive partitioning of the strain energy into distinct elastic and over-stress components, while constitutive anisotropy is introduced via a generalized structural tensor. Moreover, the evolution of the viscous strain is governed by a possibly anisotropic flow rule featuring five characteristic times. Remarkably, we show that this flow rule can be cast into a convenient variational form by taking either the contravariant or the covariant pull-back of the spatial evolution law. This structure facilitates computational implementation and avoids the issue of constraining the viscous spin.

Numerical simulations validate the model against benchmark behaviours, successfully reproducing stress relaxation, creep, and hysteresis. Additionally, non-homogeneous simple shear tests reveal a non-monotonic Poynting effect that is highly sensitive to fibre distribution and relative fibre-matrix stiffness. Finally, we discuss the framework's applicability to modeling the viscoelastic mechanics of reproductive tissues.

Speaker: Giulio Lucci (Sapienza University of Rome)

18:00 A FEniCSx Implementation of the Deep Rheological Element for Finite-Strain Nonlinear Viscoelasticity

This work introduces a computational framework for the finite-element simulation of finite-strain nonlinear viscoelasticity using the Deep Rheological Element (DRE). The DRE represents a neural-network-augmented dashpot whose viscosity function is learned from data while remaining embedded in a thermodynamically consistent architecture. We integrate this element into a finite-strain Generalized Maxwell Model (GMM) based on the multiplicative decomposition of the deformation gradient, enabling the prediction of complex phenomena, such as the Payne effect in filled elastomers.

The implementation is developed within the FEniCSx environment, where the entire finite-strain formulation, including the neural-network-driven viscosity, is expressed directly in the Unified Form Language (UFL). For incompressible isotropic materials, the deviatoric viscosity is expressed as an isotropic scalar function of the invariants of the total and viscous unimodular left Cauchy–Green deformation tensors. In this demonstrative implementation, the general invariant set is reduced to a dependence on the single invariant $J_2 = \| \mathbf{T}_e^D \|$, allowing the model to recover a power-law behavior.

The robustness of the variational implementation is assessed through two main numerical experiments: (i) a shear-block benchmark under amplitude-sweep oscillatory loading to verify storage and loss moduli against analytical DRE predictions, and (ii) a 3D cylinder subjected to large-angle torsion. In the latter, the DRE accurately reproduces the torque and normal force responses, demonstrating numerical stability in realistic boundary-value problems with heterogeneous deformations.

Speaker: Federico Califano (Sapienza University of Rome)

19:00 → 22:00 Pub Crawl by Y-SIMAI

To partecipate follow the instructions available here: https://events.dm.unipi.it/event/331/page/51-social-events

Friday 5 June

09:00 → 10:45 MS01 - Advanced Numerical Methods and Models for Coupled Solid Problems and Multiphysics Systems

Advanced Numerical Methods and Models for
Coupled Solid Problems and Multiphysics Systems

09:00 Improving the accuracy of the Fictitious Domain method in domains with embedded inclusions.

We introduce a novel unfitted finite element method for elliptic problems posed on domains with embedded inclusions. The proposed approach extends the standard Fictitious Domain framework by enforcing a smooth extension of the solution inside the fictitious region. This feature allows the method to attain optimal convergence rates in settings where classical Fictitious Domain formulations may exhibit reduced accuracy. The method is simple to implement, does not require any enrichment of the finite
element space, and provides an excellent trade-off between computational cost and accuracy. We analyze the method within the framework of generalized saddle-point problems, establishing the well-posedness of both the continuous and discrete formulations. An inexact integration strategy is employed for the coupling terms, and analytical estimates for the resulting quadrature errors are derived. Although the inexact integration introduces additional lower-order error terms for continuous piecewise linear finite elements, numerical experiments in two and three dimensions show that these effects are not dominant at practical refinement levels, and optimal convergence rates are observed.

Speaker: Gregorio Casella (Politecnico di Milano)

09:15 Fully coupled nonlinear electromechanical user-element framework for 3D-printed lead-free ferroelectric ceramics

Additive manufacturing of piezoceramics enables the acquisition of high resolution lead-free piezoelectric architected microgeometries that are difficult to realize with conventional processing. To exploit these design freedoms, predictive multiphysics models must capture the electromechanical coupling together with the non linear, history dependent response typical of ferroelectric materials.

We present a user element (UEL) implementation in Abaqus for fully coupled electromechanical simulations of piezoelectric solids, accounting for both direct and inverse effects. The element uses a hexahedral 8 node formulation with 4-DOF per node. At each integration point, the constitutive update is driven by the local mechanical and electric fields and is handled through a Jiles–Atherton type phenomenological model adapted to ferroelectric behavior.
In the proposed framework, the polarization is split into irreversible and reversible parts, $P={P}^{\mathrm{irr}}+{P}^{\mathrm{rev}}$ with the reversible contribution defined as ${P}^{\mathrm{rev}}=c{P}^{\mathrm{an}}-{P}^{\mathrm{irr}}$, where c is the reversibility coefficient and $P^{\mathrm{an}}$ is the anhysteretic polarization. This contribution is modeled through a Langevin relation that is driven by an effective electric field $E_{\mathrm{eff}}$, which combines the applied electrical field with internal electromechanical interactions. The irreversible evolution law drives ${P}^{\mathrm{irr}}$ toward ${P}^{\mathrm{an}}$ in a history dependent manner, capturing memory and minor loop behavior. The updated polarization is coupled to strain through electrostrictive terms, yielding a nonlinear, path dependent electromechanical response.
The set of internal variables evolves with the load history and enforces the nonlinear relationship between the electric field, polarization, and strain. In representative cyclic electrical and combined electromechanical loading cases, the model reproduces the characteristic hysteresis and strain “butterfly” loops observed in ferroelectric ceramics.

The proposed framework targets efficient simulation of components with complex microarchitectures produced by 3D printing, providing a route to virtual prototyping and parameter exploration prior to fabrication. Ongoing work focuses on validation across a set of loading paths and applying the model to lattice-like and porous geometries.

Speaker: Pieter Laureys (Politecnico di Milano)

09:30 Fluid-Structure Interation for Hydrofoils

This contribution describes a Fluid–Structure Interaction (FSI)
solver based on a partitioned steering approach. The structural
partecipant is modeled using linear elasticity and advanced in time with
a one-step theta method. Such a model is coupled with a numerical
method for incompressible quasi-potential flows around three-dimensional
lifting streamlined bodies (Cattarossi et al., 2026).

The discretization methods for the solid and fluid problems are based on
the Finite Element Method (FEM) [deal.II] and the collocation Boundary
Element Method (BEM) [$\pi$-BEM, (Giuliani et al., 2018)], respectively.

The interaction between the structural and fluid solvers is managed by
means of preCICE (Chourdakis, Davis, Rodenberg, Schulte, Simonis,
Uekermann et al., 2022), a fully parallel library for multi-physics
surface coupling. It operates as an independent black-box code handling
a mesh-to-mesh data mapping, temporal coupling, and convergence
acceleration.

To ensure stable and accurate exchange of interface quantities,
particular attention is paid to defining consistent coupling variables
and treating the mismatch on the two different meshes. In particular,
the displacement and velocity fields provided by the structural solver
are projected onto the fluid interface, while the pressure loads
calculated from the boundary element formulation are transferred to the
structure. Within preCICE, these operations are complemented by
fixed-point acceleration, implicit coupling iterations, and relaxation
strategies that ensure robustness.

Numerical results and application cases are be presented to demonstrate
the effectiveness of the approach proposed.

Speaker: Luca Cattarossi (Scuola IMT Alti Studi Lucca)

09:45 Carbonation-Driven Cracking in Concrete: A Multiphysics Phase-Field Approach

Carbonation is a major degradation process affecting cementitious materials, with significant implications for the durability and service life of concrete structures. Under atmospheric exposure, carbon dioxide (CO$_2$) penetrates the partially saturated pore network, dissolves in the pore water, and initially reacts with portlandite (Ca(OH)$_2$) to form calcium carbonate (CaCO$_3$). As carbonation progresses, the calcium silicate hydrate (C-S-H) phase undergoes decalcification, accompanied by further precipitation of calcium carbonate. These coupled chemical reactions lead to pronounced modifications of the mineralogical composition and pore structure of concrete, inducing volumetric shrinkage, changes in transport properties, and the development of internal stresses that promote crack initiation and propagation.

In this study, we present a fully coupled modelling framework that integrates reactive CO$_2$ transport within concrete with a phase-field formulation of fracture. The model explicitly captures the sequential dissolution of portlandite and the progressive decalcification of C-S-H, together with the associated mineralogical transformations and porosity evolution. Shrinkage strains resulting from carbonation-induced reactions are incorporated as driving mechanisms for damage initiation and crack growth. The coupling between chemical degradation, moisture transport, and fracture mechanics enables the description of feedback effects between reaction kinetics, evolving material properties, and mechanical damage.

By providing a mechanistic representation of the interplay between carbonation reactions, pore structure evolution, and fracture processes, the proposed framework offers a predictive tool for assessing carbonation-induced damage and its impact on the long-term durability of cementitious materials exposed to atmospheric conditions.

Speaker: Lorenzo Mingazzi (Università degli Studi di Parma)

10:00 A Partitioned Solver for the Fluid-Solid Interaction of Lightweight Flexible Structures

The characteristic behaviour of highly flexible structures, such as membranes and cable-like systems, in Fluid–Solid Interaction (FSI) conditions, typically involves strong fluid–structure nonlinear coupling due to the low solid-to-fluid mass ratio, the bending rigidity of the structure, and the Reynolds number of the problem. Additional nonlinearities include large structural displacement and those of material.

This work presents highlights from ongoing research aimed at developing a fully open-source tool for simulating the FSI response of this class of structures. The proposed framework relies on coupling Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM) solvers. Currently, we have developed a workflow for a partitioned approach, using an Arbitrary Lagrangian–Eulerian (ALE) formulation. Within this context, the choice of simulation and acceleration method parameters as well as moving-mesh approach is crucial, given their critical role in determining the convergence and robustness of the coupled simulation.

In this talk, we will present the results of a series of FSI simulations of flapping flag-like structures. The first objective is to identify the most critical numerical strategies for obtaining stable and accurate solutions. The second objective is to propose possible improvements to establish a robust and reproducible workflow for the FSI analysis of highly flexible structures. Finally, we will conclude by discussing future developments based on alternate mesh-moving techniques or Immersed/Embedded Boundary Methods (IBM/EBM).

Speaker: Mario Pistis (University of Cagliari)

10:15 Mass-zero constrained molecular dynamics for electrostatic processes

The evaluation of electrostatic forces remains a major computational challenge in molecular dynamics (MD) simulations of large-scale systems. Direct pairwise calculations scale as $\mathcal{O}(N^2)$, while long-range interactions under periodic boundary conditions require dedicated algorithms. The current method of choice, Particle Mesh Ewald (PME)[1], achieves $\mathcal{O}(N \log N)$ scaling via fast Fourier transforms; however, its reliance on global communication becomes a bottleneck at very large processor counts.
We present Poisson MaZe[2], a real-space method to compute electrostatic forces within the Mass-Zero constrained dynamics (MaZe) framework[3], developed as a C-based Python package. The method is based on a finite-difference discretization of the Poisson partial differential equation (PDE) for the electrostatic potential, enforced as a dynamical constraint self-consistently coupled to particle dynamics.

The talk addresses three key aspects of the approach. First, we validate the method through realistic simulations of molten NaCl, demonstrating accurate reproduction of structural and transport properties. Second, we examine computational performance: when combined with a multigrid solver, Poisson MaZe achieves linear scaling with system size and converges in substantially fewer cycles than a direct multigrid solution of the Poisson equation. Third, we discuss its numerical properties, including time reversibility, stationarity, conservation of total momentum, and long-time behavior of the energy.

Building on this foundation, we present extensions to implicit-solvent models governed by the Poisson–Boltzmann (PB) equation. To handle the media discontinuities inherent to PB-like models, we employ a numerical treatment analogous to the primal-mixed FEM method. We address the linear case and outline ongoing developments toward nonlinear electrostatic coupling through a field-dependent permittivity $\varepsilon(\mathbf{E})$, with the overarching
goal of improving the electrochemical coupling in the solvent region.

[1] Darden et al., J. Chem. Phys. 98, 10089 (1993).
[2] Troni et al., J. Chem. Phys. 163, 214106 (2025).
[3] Coretti et al., J. Chem. Phys. 157, 214110 (2022).

Speaker: Federica Troni (Centre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne (EPFL))

10:30 Quasi-singular quadrature strategy for BEM-based contact detection

A recent work by Areias et al. [ASA23] shows how it's possible to detect contact by solving the scalar Screened Poisson equation $$ \Delta \phi (\mathbf{x}) - \operatorname{k}^2 \phi(\mathbf{x}) = 0 \qquad \text{for } \operatorname{k} \in \mathbb{R}$$ with constant boundary conditions. Solving this equation in a domain $\Omega$ of arbitrary shape allows us to obtain an Approximate Distance Function (ADF) to uniquely establish whether the boundary of the domain contacts itself at certain points. In this work we explore a BEM-based formulation of this approach, which avoids the discretization of the whole bulk of the domain. For this purpose, we successfully implement the resolution of the Screened Poisson equation in $\pi$-BEM, a parallel boundary element method solver developed by Giuliani et al. [GMH18].

We notice that in the near contact configuration two cells that are topologically distant from each other become geometrically close. This highlights the fact that an inadequate numerical treatment of quasi-singular integrals may increase substantially the global computational effort. To address this issue, we develop a specific quasi-singular quadrature strategy based on a variable transformation technique, to handle all cases close to contact. That is, we change the coordinates of integration from cartesian to spherical. This way, the Jacobian from the change of coordinates compensates the singular kernel, regularizing the integrand.

References

[ASA23] P. Areias, N. Sukumar, and J. Ambrosio. Continuous gap contact formulation based on the screened poisson equation. Computational Mechanics, 72:707–723, 2023.

[GMH18] N. Giuliani, A. Mola, and L. Heltai. π-BEM: A flexible parallel implementation for adaptive, geometry aware, and high order boundary element methods. Advances in Engineering Software, 121:39–58, 2018.

Speaker: Irene Nesi (Scuola IMT Alti Studi Lucca)

09:00 → 10:45 MS07.1 - Recent Advances in Data-Driven Surrogate Modeling

09:00 Learning adaptive basis representations for parametrized PDEs with Deep Orthogonal Decomposition

We present Deep Orthogonal Decomposition (DOD) [1], a novel technique for dimensionality reduction and reduced order modeling of parametrized PDEs. The DOD consists in a deep neural network approximating the solution manifold through a continuously adaptive local basis. In contrast to global techniques such as Proper Orthogonal Decomposition (POD), the local adaptivity of the learned basis allows DOD to mitigate the Kolmogorov barrier, significantly broadening its applicability to challenging nonlinear problems. Additionally, thanks to the orthogonal structure of the latent space, DOD ensures a tight control on error propagation and enhanced interpretability, resulting in an appealing alternative to deep autoencoders. Beyond steady parametric settings, the proposed framework naturally extends to time-dependent PDEs by treating time as an additional input variable, allowing the learned basis to adapt continuously to the evolving system state. From this perspective, DOD can be interpreted as a data-driven tool for learning low-dimensional representations of nonlinear dynamical systems. The methodology is analyzed both theoretically and practically. On the one hand, we establish a connection between the truncation error of the DOD and a spectral gap condition related to the solution manifold [2], whereas on the other with assess the performances of the DOD on a set of numerical experiments involving nonlinear PDEs with parametrized geometries and high-dimensional parameter spaces [1].

References
[1] NR Franco, A Manzoni, P Zunino, JS Hesthaven. Deep orthogonal decomposition: a continuously adaptive neural network approach to model order reduction of parametrized partial differential equations . Advances in Computational Mathematics, accepted, 2026.
[2] NR Franco. Measurability and continuity of parametric low-rank approximation in Hilbert spaces: linear operators and random variables. Revista Matemática Complutense, pages 1–42, 2025.

Speaker: Nicola Rares Franco (MOX, Dipartimento di Matematica, Politecnico di Milano)

09:15 Benchmarking the translation invariance of Neural Operators for the FitzHugh-Nagumo model

Neural Operators (NOs) are a deep learning technique designed to learn the solution operator of ordinary and partial differential equations (ODEs and PDEs). Their application to stiff ionic models, which are essential for describing excitable cells in cardiac and neural systems, is a field of growing interest. This study investigates the ability of different NOs architectures to capture the stiff dynamics of the one-dimensional FitzHugh-Nagumo (FHN) model. A key contribution of this work is the evaluation of translation invariance and out-of-distribution generalization. We propose a novel, computationally efficient training strategy in which models are trained using an applied current with varying spatial locations and intensities at a fixed time. These models are then tested on a dataset involving complex translations in both time and space. Furthermore, we conducted a thorough study to evaluate the ability of NOs to learn these translated dynamics and their relative efficiency in terms of training and inference performance.

Speaker: Luca Pellegrini (University of Pavia)

09:30 Learning the continuous-time dynamics: from trajectories to velocities

Learning nonlinear continuous-time dynamical systems is a central problem in many fields of science and engineering. Deep learning architectures characterized by a continuous-time inductive bias, such as Neural ODEs, have seen widespread adoption in this context, with applications ranging from low-dimensional dynamical systems modeling to data-driven order reduction for time-dependent PDEs by relying on suitable nonlinear dimensionality reduction strategies. Despite many advantages stemming from their continuous-time inductive bias, including mathematical interpretability and time super-resolution, they rely on a simulation-based training procedure, which, whether employed directly in state-space or in a latent space of reduced dimension, requires unrolling the predictions over multiple steps by means of numerical integration. Rollout-based training, while motivated by empirical evidence for providing stable predictions, involves high computational costs and memory requirements due to backpropagation through time, which are further compounded by higher-order numerical integration of the Neural ODE. In this talk, we first address the pitfalls of rollout-based training in the context of learning continuous-time dynamics, analyzing the bias introduced by the numerical solver when unrolling predictions in the infinite-horizon limit, thereby hindering proper identification of the underlying dynamics. Then, we discuss the advantages of a velocity-based training objective, by proposing the adoption of a stochastic objective that results in a higher-order approximation of the population risk, whose approximation properties are characterized. Numerical experiments, carried out in the context of dynamical systems and time-dependent PDEs, validate the efficiency of the proposed approach, highlighting faster convergence and improved generalization compared to a range of rollout-based training strategies.

[1] N. Farenga, S. Fresca, S. Brivio, A. Manzoni, On latent dynamics learning in nonlinear reduced order modeling, Neural Networks, Volume 185, 2025, 107-146, ISSN 0893-6080.

[2] N. Farenga, A. Manzoni, In preparation, 2026.

Speaker: Nicola Farenga (Politecnico di Milano)

09:45 Randomized Low-Rank Natural Gradient Methods for Scalable Neural PDE Learning

Natural Gradient Descent (NGD) has recently gained attention as an effective optimization approach for deep-learning-based solvers of partial differential equations (PDEs), particularly Physics-Informed Neural Networks (PINNs). By leveraging the geometric structure of the neural network parameter manifold, NGD can achieve substantially faster convergence in terms of iteration count compared to standard first-order optimization methods. However, widespread practical use has been hindered by the high computational cost of constructing and inverting the Gramian matrix, which scales cubically with the number of network parameters.

In this talk, we introduce a computationally efficient NGD framework for neural PDE solvers that addresses these challenges through a combination of matrix-free formulations and low-rank preconditioning techniques. We generalize matrix-free NGD to a wide class of neural PDE models, including PINNs, Variational PINNs, Finite Element Interpolated Neural Networks, and Robust VPINNs, as well as to general choices of underlying metrics. Exploiting the empirically observed low-rank structure of the Gramian matrix, we design preconditioners based on randomized numerical linear algebra methods, including Nyström approximations and partial pivoted Cholesky factorizations. These approaches significantly accelerate convergence of the inner iterative solvers while maintaining manageable memory and computational requirements.

We provide a systematic comparison of multiple NGD variants—explicit inversion, unpreconditioned matrix-free schemes, and several preconditioned strategies—analyzing both theoretical complexity and practical performance to identify regimes where each method is most effective. We further discuss efficient implementations based on automatic differentiation and offer practical guidelines for integrating NGD into existing optimization and autodiff frameworks. Finally, we benchmark the proposed methods against state-of-the-art optimizers across a range of PDE problems, demonstrating notable reductions in training time alongside improved accuracy and robustness. Overall, the results establish low-rank preconditioned NGD as a scalable and competitive optimization paradigm for modern neural PDE solvers.

Speaker: Ivan Bioli (Università di Pavia)

10:00 Separable Representations of Optimal Value Functions via Neural Networks

In this talk, we discuss how separable structures provide an effective approach to approximating high-dimensional optimal value functions. The key structural property that enables such approximations is a decaying sensitivity between subsystems, meaning that the influence of one state variable on another diminishes with their graph-based spatial distance. This property makes it possible to construct separable approximations of the optimal value function as a sum of localized contributions. We further demonstrate that these separable approximations admit efficient neural network representations, where the number of parameters grows only polynomially with the state space dimension. These results highlight how structural properties of the problem can be leveraged to obtain scalable neural network representations, thereby mitigating the curse of dimensionality in optimal control.

Speaker: Luca Saluzzi (Università degli studi di Ferrara)

10:15 Step-by-Step Time-Discrete PINNs: Embedding Time Integrators into Neural Networks

Physics-Informed Neural Networks (PINNs) are increasingly adopted as data-driven surrogate models for partial differential equations (PDEs), but standard formulations often rely on continuous spatio-temporal approximations and may face training instabilities in time-evolution and stiff regimes. In this contribution, we present a step-by-step time-discrete PINN methodology that produces solutions discrete in time and continuous in space, by embedding classical one-stage implicit time integrators directly into the network design. The approach establishes an explicit link between network outputs and the numerical approximations generated by implicit Euler and Crank–Nicolson schemes, leading to loss functions that enforce the time-marching structure while naturally incorporating the initial condition. We also formalize the comparison with existing Runge–Kutta-based time-discrete PINNs, highlighting how the proposed construction overcomes the need for re-training at each time step and avoids high-stage RK designs. The result is a surrogate modeling framework that inherits desirable numerical properties from the embedded integrator, while retaining the flexibility of neural approximators for fast inference over the spatial domain. The methodology is illustrated on a nonlinear diffusion–reaction sustainability PDE model, used here as a representative benchmark to discuss design choices and practical implementation aspects.

Speaker: Carmine Valentino (University of Salerno)

10:30 Space-time continuous pde forecasting using equivariant neural fields

Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as grid-agnosticity and space-time-continuous dynamics modelling, this approach limits the ability to impose known constraints of the PDE on the solutions--such as symmetries or boundary conditions--in favour of modelling flexibility. Instead, we propose a space-time continuous NeF-based solving framework that-by preserving geometric information in the latent space of the Conditional NeF-preserves known symmetries of the PDE. We show that modelling solutions as flows of pointclouds over the group of interest improves generalization and data-efficiency. Furthermore, we validate that our framework readily generalizes to unseen spatial and temporal locations, as well as geometric transformations of the initial conditions-where other NeF-based PDE forecasting methods fail-, and improve over baselines in a number of challenging geometries.

Speaker: Riccardo Valperga (AI4I)

09:00 → 10:45 MS17 - Inverse Problems in Structural Engineering

09:00 The Calderón problem with finitely many random measurements

The Calderón problem consists in recovering an unknown parameter of a partial differential equation from boundary measurements of its solution. While global uniqueness is well-established for the full Dirichlet-to-Neumann operator, corresponding to infinitely many boundary measurements, practical applications, such as EIT, operate with finite and discrete data.

In this realistic setting, the unknown parameter is assumed to lie in a finite-dimensional space, and the boundary data are restricted to a finite family of Dirichlet-Neumann pairs. This reduction leads to a fundamental question regarding sample complexity: what is the minimal number of measurements M required to reconstruct a d-dimensional unknown? Due to the non-linearity and severe ill-posedness of the problem, existing deterministic results often yield sample complexity estimates that are exponential in d.

In this work, we address this question using randomized boundary data. Instead of deterministically choosing a finite number of boundary data from a fixed orthonormal basis on the boundary of the domain, we take random linear combinations of such basis elements. We prove that this approach ensures almost sure uniqueness with a number of measurements M that is merely proportional to the dimension of the parameter space d, significantly improving upon current deterministic bounds.

Speaker: Simone Sanna (MaLGa center - Università degli studi di Genova)

09:15 An integrated framework for shape-sensing and damage identification based on inverse Finite Element Method and Modal Expansion

Inverse problems are central to modern Structural Health Monitoring (SHM), where the health state of a structure must be inferred from measured responses and the onset of damage must be promptly identified. In this context, increasing attention has been devoted to real-time SHM strategies, particularly in view of Digital Twin (DT) applications for remote structural monitoring.
Within DT-enabled SHM, shape sensing is a key capability. Among available approaches, the inverse Finite Element Method (iFEM) has emerged as a highly accurate strategy for reconstructing full-field structural displacements from strain measurements. However, this accuracy typically requires dense back-to-back sensor layouts, which are often difficult to implement in practical applications. Two complementary strategies mitigate this limitation: the Single Sensor Based (SSB) iFEM, which enables single-sided sensor configurations, and the Modal Virtual Sensor Expansion (MVSE), a strain pre-extrapolation technique that generates virtual strain sensors data.
Recent real-time monitoring experimental applications have shown that iFEM can effectively support DT implementations. Nevertheless, iFEM alone addresses the shape-sensing task only. To endow an iFEM-based DT with SHM functionality, it must be integrated with a damage identification procedure. To address this gap, this work presents an experimental application on a thin-walled C-section beam instrumented with a single-sided sensor configuration. Real and MVSE-expanded strain data are combined to feed SSB-iFEM and perform real-time monitoring. In parallel, a damage identification procedure is implemented using MVSE-reconstructed strains.
The proposed framework demonstrates that the integration of MVSE, SSB-iFEM, and a damage identification procedure is a practical SHM strategy for real-time applications, enabling DT-based monitoring with a reduced number of sensors.

Speaker: Vincenzo Biscotti (Politecnico di Torino)

09:30 Inverse Load Identification via Reconstruction of Structural Strain Response Maps

This contribution addresses the identification of concentrated static loads from strain measurements in geometrically nonlinear composite plates instrumented with embedded Fiber Bragg Grating (FBG) sensors. Since a rigorous investigation of this problem is missing in the literature, a mathematical framework is formulated from first principles.
A data-driven problem inversion algorithm is developed in which the external load is parametrized by a finite-dimensional vector, while the structural response is modeled as a nonlinear mapping from the load parameter space to the strain measurement space. This mapping is reconstructed from calibration data using interpolation and regression techniques. The unknown load parameters are then estimated by minimizing a distance functional in the output space.
The performance of the algorithm is first assessed through analytical and numerical case studies to identify the critical factors governing accuracy. Subsequently, the method is validated experimentally through the identification of static concentrated loads applied to a fully clamped carbon fiber plate.
Results indicate that data-driven load identification from strain measurements is feasible only under well-defined conditions. In particular, identification accuracy is primarily governed by sensor placement, calibration sampling density, and data quality. Sensors should be positioned outside the region of interest to reduce local response complexity and improve reconstruction robustness. Moreover, the experimental calibration data must be adequately processed to approximate the system response expected during real world deployment of the load identification algorithm.

Speaker: Lorenzo Cioli

09:45 Towards the Identification of Moving Loads from Distributed Strain Measurements in Composite Plates

This study investigates the dynamic response of a composite plate subjected to a pressure wave generated by a moving source, with the primary objective of identifying equivalent external loads from local strain measurements. The research focuses on reconstructing dynamic load parameters by analyzing signals acquired from a discrete array of Fiber Bragg Grating (FBG) sensors integrated within the laminate.

The identification of external loads from local measurements represents a challenging inverse problem, often characterized as ill-posed and non-unique. To ensure tractability, the pressure field is modeled as a cylindrical wavefront propagating in a sub-resonant regime. The analysis assumes linear structural behavior and small deformations, while neglecting fluid-structure interaction effects. The goal is to identify a set of equivalent parameters, including peak amplitude and the kinematic variables governing the source motion.

The proposed methodology integrates analytical modeling with Finite Element Method (FEM) simulations of the transient structural response. The analytical framework is built upon Kirchhoff–Love theory for thin plates and is derived through an energetic formulation (minimizing the action functional), ensuring consistent dynamic equations that account for the anisotropic stiffness of the composite.

Transient simulations were performed for various trajectories (centered and eccentric) to support the inverse identification strategy. A decoupled approach is adopted: kinematic parameters are first estimated by exploiting structural symmetries and qualitative features of the strain-time histories, while the load amplitude is subsequently determined through a scaling procedure. This work serves as a foundational step for structural health monitoring (SHM) and load reconstruction in instrumented composite structures.

Speaker: Gabriele Venturi (Università di Pisa - Scuola Superiore Sant'Anna)

09:00 → 10:45 MS18 - Modeling of Elastic Multiphase Structures for Bio-Mechanics

09:00 A geometric surface PDE model for cell–nucleus translocation through confinement

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in navigating narrow pores or highly constrained spaces.

In this talk, I will present a novel geometric surface partial differential equation (GS-PDE) framework in which the cell plasma membrane and the nuclear envelope are modeled as evolving energetic closed surfaces governed by force-balance equations. To validate the model, we replicate a biophysical experiment using a microfluidic device that imposes compressive stresses on cells driven through narrow microchannels under a controlled pressure gradient. I will discuss the results of our parametric sensitivity analysis, which highlights the dominant influence of specific parameters, such as surface tension and confinement geometry, as key determinants of translocation efficiency.

Finally, I will show how this framework, while tailored to a specific experimental setup for validation, provides a robust, flexible, and generalizable tool for investigating the broader interplay between cell mechanics and confinement, laying the groundwork for integrating more complex biochemical processes like active migration.

Speaker: Francesca Ballatore (Université Côte d'Azur)

09:15 The role of remodeling and of the interstitial fluid in the description of “boundary effects” in multicellular aggregates

Multicellular aggregates represent a wide class of hydrated soft biological media, in which the interplay between the flow of the interstitial fluid and the reorganization of the internal structure (remodeling) dictate the overall mechanical and hydraulic properties of the aggregates [1].

An interesting phenomenon occurring, for instance, when indentation and torsion tests are performed on multicellular aggregates is the formation of boundary-layers nearby the points of contact between experimental apparatus and specimen [2]. There, the ductility properties and the hydraulic behavior of the aggregates can significantly deviate from the ones found in its interior, and some authors attribute these effects to local changes in the boundary curvature [3].

With the objective of capturing these boundary effects, in this presentation we adapt the strain-gradient plasticity theory by Gurtin and Anand [4] to describe the remodeling of a biphasic medium in non-Darcian regime. In doing so, we follow the main steps taken in [5], where we give particular emphasis on the thermodynamical and computational aspects of the work.

References
[1] Giverso, C., Preziosi, L., “Modelling the compression and reorganization of cell aggregates”, Math Med Biol, 29(2), 181–204 (2012).
[2] Fleck, N. A., and Hutchinson, J. W. (1997). Strain gradient plasticity. Advances in Applied Mechanics, 33, 295–361.
[3] Callens, S. J., Uyttendaele, R. J., Zajac, M., and Zadpoor, A. A. (2020). Substrate curvature as a design parameter for complex tissue structures. Biomaterials, 232, 119739.
[4] Gurtin, M. E., Anand, L., “A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part II: Finite deformations”, Int. J. Plas., 21(12), 2297–2318 (2005).
[5] Giammarini, A., Pastore, A., Ramírez-Torres, A., and Grillo, A., “A first-gradient approach to the remodeling and fluid flow in saturated porous media”, Math. Mech. Solids, 30(9), 2185–2223 (2025).

Speaker: Andrea Pastore (Politecnico di Torino)

09:30 Stretch Reversal under Biaxial Loading in Fibre-Reinforced Soft Tissues

When fibre-reinforced soft biological tissues undergo biaxial tension, it is generally assumed that both in-plane stretches will increase monotonically with the applied stress. However, under specific combinations of fibre architecture and loading biaxiality, a counterintuitive kinematic phenomenon of stretch reversal may occur, where one principal stretch reaches a local maximum and subsequently decreases, even as the applied biaxial loads continue to grow.

We develop a unified analytical framework to define the specific conditions under which this reversal occurs in anisotropic hyperelastic materials. Our findings indicate that stretch reversal arises from a fundamental geometric competition between the compliant isotropic matrix, the anisotropic fibre reinforcement, and the incompressibility constraint. Specifically, using an exponential constitutive model, we identify a critical fibre stiffness threshold that separates a regime of immediate transverse contraction from one permitting stretch reversal.

To bridge theoretical predictions with experimental testing, we implement a finite element formulation for cruciform specimens and compare our computational predictions with experimental biaxial testing data from soft tissues. Finally, we demonstrate how the high sensitivity of this reversal phenomenon to fibre architecture can be actively exploited to formulate a robust, sequential parameter-identification strategy.

Speaker: Giulio Lucci (Sapienza University of Rome)

09:45 Swelling phenomena in the vitreous body

The vitreous body is a transparent, highly hydrated tissue of spherical shape that is located between the lens and the retina in the ocular apparatus. In healthy conditions, the vitreous fills the ocular cavity and acts as a mechanical damper for the fluid’s motions in response to the saccadic eye movements [1]. The aging process, however, can impact negatively its biological functionality, making it opaque and unable to dampen the fluid shear stresses, due to the liquefaction of the vitreous and the formation of fluid pockets inside the tissue [2].
We propose a chemo-mechanical model that describes liquefaction as an alteration to the swelling phenomena occurring in the tissue under study, which is studied as a solid-fluid mixture, so that as time passes some regions of the vitreous are no more able to contain the fluid that was previously swollen. In particular, we investigate the relation between the volume occupied by the fluid and the balance of the osmotic and elastic forces.

References:
[1] M. Levin and N. Cohen, “The effects of aging on the mechanical properties of the vitreous”, Journal of Biomechanics, 2021.
[2] J. Sebag et al., 2014, “Vitreous: in Health and Disease”. Springer New York.

Speaker: Alessandro Giammarini (Politecnico di Milano)

10:00 Periodic beading in damaged axons: the role of surface elasticity

The Plateau--Rayleigh instability shows that a cylindrical fluid flow can be destabilized by surface tension. Similarly, capillary forces can make an elastic cylinder unstable when the elastocapillary length is comparable to the cylinder's radius. This is the case of axons: in the presence of several neurological pathologies, such as multiple sclerosis, Alzheimer's, and Parkinson's diseases, axons exhibit the formation of non-physiological, periodic bulges along their whole length. Experimental evidence suggests that the mutual interaction between the microtubule disassembly and the active contractility of the axonal cortex could represent the cause of this abnormal morphological deformation. While existing models, hypothesizing that surface tension is independent of the deformation of the solid and neglecting variations due to surface stretch, predict a single isolated bulge as the result of an instability, experiments reveal a periodic sequence of bulges spaced out by thinned regions, a phenomenon known as beading instability.

In this talk, we model axons as cylindrical bodies and assume that surface tension arises from the deformation of material particles near the free surface, treating it as a pre-stretched elastic surface. Using the theoretical framework proposed by Gurtin and Murdoch, we show that a cylindrical solid can undergo a mechanical instability with a finite critical wavelength if the body is sufficiently soft or axially stretched, explaining in mechanical terms the axonal beading phenomenon. Post-buckling numerical simulations reveal a morphology in qualitative agreement with experimental observations. Period-halving secondary bifurcations are also observed.

Speaker: Francesco Magni (International School for Advanced Studies (SISSA))

10:45 → 11:15 Coffee break

11:15 → 13:00 MS07.2 - Recent Advances in Data-Driven Surrogate Modeling

11:15 Hierarchical Model Reduction for Patient-Specific Vascular Flows

Hierarchical Model (HiMod) reduction is a mathematical technique developed to accurately model problems exhibiting an intrinsic dominant directionality (e.g., in pipe-like domains) at an affordable computational effort. HiMod reduction has been successfully employed in several applications, including hemodynamics [1] and acoustic wave propagation [2].

The approach relies on a separation-of-variables paradigm that allows the leading fiber to be treated independently from the transverse dynamics. The leading dynamics is discretized using spline-based basis functions, enabling the treatment of curvilinear centrelines and complex geometries, such as vascular domains [1]. The transverse dynamics are described through a modal basis expansion. The full-order model is thus reduced to a system of coupled 1D equations whose dimension depends on the number of modes [3].

Recent developments have established the inf-sup stability of the HiMod discretization and enabled the development of a MATLAB HiMod library for fluid dynamics applications. In this talk, HiMod reduction is employed to handle patient-specific vascular geometries reconstructed from medical images, including stenotic coronary arteries and abdominal aortic aneurysms. Comparisons with full-order solutions show that HiMod is a reliable tool for biomedical analyses, balancing computational efficiency and accuracy in evaluating clinically relevant hemodynamic quantities. Furthermore, a preliminary investigation about the integration of machine learning algorithms in HiMod reduction is carried out to further enhance the methodology performance, with the goal of enabling real-time simulations.

[1] Brandes Costa Barbosa, Y. A., Perotto, S. (2020). Hierarchically reduced models for the Stokes problem in patient-specific artery segments. Int. J. Comput. Fluid Dyn., 34(2), 160-171.
[2] Gentili, G. G., et al. (2022). Efficient modeling of multimode guided acoustic wave propagation in deformed pipelines by hierarchical model reduction. Appl. Numer. Math., 173, 329-344.
[3] Perotto, S., Ern, A., Veneziani, A. (2010). Hierarchical local model reduction for elliptic problems: a domain decomposition approach. Multiscale Model. Simul., 8(4), 1102-1127.

Speaker: Erika Temellini (Politecnico di Milano)

11:30 DATA-DRIVEN REDUCED ORDER MODEL FOR LAMINAR FLUID-STRUCTURE PROBLEM

Fluid-Structure Interaction (FSI) plays a crucial role in predicting the dynamic response of systems across diverse engineering applications, from aeroelasticity to biomechanics. While high-fidelity Computational Fluid Dynamics (CFD) accurately captures the complex physics of these moving-boundary problems, the computational cost of resolving the deforming domains at every time step is very expensive for analysis and design.

We address this limitation by presenting an efficient data driven Reduced Order Model (ROM) implemented within the ITHACA-FV open source library. Our approach achieves significant dimensionality reduction by constructing a low dimensional subspace using Proper Orthogonal Decomposition (POD) and projecting the governing fluid equations via a Galerkin method.

To handle the continuous mesh deformation governed by the Arbitrary Lagrangian Eulerian (ALE) formulation we implement a Radial Basis Function (RBF) interpolation strategy. We perform RBF interpolation to train the reduced fluid operators based on the mesh deformation parameters. During the online phase we then evaluate these trained operators directly for each new deformed mesh configuration. This approach completely bypasses the expensive online construction and matrix assemblies of those operators at every time step.Furthermore the fluid and structural domains are integrated via a robust strong coupling algorithm extending partitioned solver approaches [1]. The structural dynamics are resolved using the Newmark time integration scheme to maintain numerical stability and strict kinematic compatibility at the interface.

Applied to the benchmark case of laminar flow around a moving cylinder at Re 200, the proposed framework significantly reduces the computational cost. By cutting the simulation time from 1 hour 40 minutes for the Full Order Model to just 58 seconds for the online method, this work demonstrates a fast and accurate approach for resolving complex FSI problems.

Speaker: Mazhar Shehzad (IMT School Of Advance Studies Luccq)

11:45 Reduced-Order Modeling of Steady Cylinder Flow via POD-Based Surrogate Models

Many engineering and scientific applications involve the simulation of incompressible flows around bluff bodies. Among these problems, flow past a circular cylinder is one of the most widely studied benchmark cases for understanding wake behavior and testing numerical methods. Although the geometry is simple, accurately resolving the flow often requires solving the Navier–Stokes equations with high numerical resolution. When such simulations must be repeated for different parameter values, the computational cost can become significant. Reduced-order modeling has therefore attracted considerable attention as a way to capture the essential flow behavior while reducing the cost of repeated simulations.

In this study, we develop a computational framework for the parametric analysis of steady incompressible flow past a circular cylinder. The high-fidelity simulations are performed by solving the two-dimensional steady incompressible Navier–Stokes equations on a structured grid using a finite-difference formulation. The steady solution is obtained through pseudo-transient iterations in which convective terms are treated with an upwind-biased scheme and viscous diffusion is handled explicitly. Incompressibility is enforced using a projection step that solves a pressure Poisson equation to correct the velocity field. Convergence of the solution is monitored through residual histories of the continuity and momentum equations.

To build a parametric dataset, simulations are carried out for a range of Reynolds numbers. Proper Orthogonal Decomposition (POD) is then applied to snapshots of velocity magnitude and pressure to extract the dominant flow structures and construct a reduced representation of the system. Surrogate models based on radial basis function interpolation (POD–RBF) and neural networks (POD–NN) are used to predict the reduced coefficients for new parameter values. The predictive performance of these models is assessed using a leave-one-out validation strategy, showing that the proposed framework can provide efficient and reliable predictions of the flow behavior.

Speaker: Shahid Ali (MUSAM Research Unit,IMT School for Advanced Studies Lucca ,Italy)

12:00 Efficient Bayesian Inverse UQ via Online Adaptive Gaussian Process Surrogates and Adaptive Delayed-Acceptance MCMC

Inverse uncertainty quantification (UQ) tasks, such as Bayesian parameter estimation, are computationally demanding when the forward model is a physics-based numerical solver. In particular, for PDE-governed systems, full-order discretizations (e.g., finite element or finite volume models) make conventional Markov chain Monte Carlo (MCMC) sampling prohibitively expensive due to the large number of forward evaluations required. Surrogate models can reduce this cost, but their effectiveness is often limited by the offline generation of high-fidelity training data. A natural remedy is to construct the surrogate online, i.e., concurrently with posterior sampling, so that training points concentrate in posterior-relevant regions.

We propose an adaptive delayed-acceptance MCMC method in which a Gaussian process (GP) regression surrogate provides a cheap first-stage approximation of the likelihood. The surrogate is refined sequentially during sampling, and its predictive uncertainty is used to decide when a high-fidelity model evaluation is required. The delayed-acceptance construction preserves the high-fidelity posterior as the invariant target distribution, while substantially reducing the number of expensive solver calls.

Numerical experiments on two benchmark inverse problems: (i) a mass-spring-damper system and (ii) an incompressible Navier-Stokes problem with variable geometry-demonstrate that the proposed strategy achieves accurate posterior estimates with markedly improved computational efficiency compared with standard single-stage MCMC and non-adaptive surrogate schemes.

Speaker: Filippo Zacchei (Politecnico di Milano)

12:15 Scientific Machine Learning for Forward and Inverse Problems in Cardiac Electrophysiology

Computational cardiology is based on the numerical solution of complex partial differential equations to model cardiac electrophysiology from non-invasive measurements. However, high-resolution simulations on anatomically realistic geometries are computationally expensive, whereas clinical practice demands rapid, interpretable, and application-oriented predictions. In this talk, we highlight recent developments in scientific machine learning for both forward and inverse cardiac problems, with a focus on operator learning and neural surrogate models.
We first describe operator learning strategies, in particular Fourier Neural Operators (FNOs) and Kernel Operator Learning (KOL), designed to learn the mapping from activation patterns in the physical domain to cardiac activation and repolarization times. These neural operators are trained on synthetic 2D and 3D domains as well as on a realistic left ventricle geometry. The learned operator for activation times aligns with the Eikonal formulation, while the operator predicting repolarization times has no explicit PDE analogue, showcasing the adaptability and expressiveness of data-driven operator learning.
We then focus on inverse cardiac problems, aiming at reconstructing ischemic areas and pacing sites from pseudo-ECG simulations. To this end, we employ an architecture inspired by Latent Dynamics Networks (LDNets), which serves as a fast neural surrogate of pseudo-ECG signals generated by the monodomain model. This approach enables efficient forward evaluations within an inverse learning framework on both 2D and 3D ventricular geometries.
These results illustrate how machine-learning-based surrogate and operator models can dramatically reduce computational costs for cardiac simulations and inverse reconstructions, paving the way toward clinically impactful applications.

Speaker: Edoardo Centofanti (University of Pavia)

12:30 Hybrid Physics–Data-Driven Reduced Order Surrogate for Turbulent Flows on Collocated Grids

The construction of reliable surrogate models for turbulent flows remains a major challenge in scientific machine learning. While projection-based Reduced Order Models (ROMs) provide mathematically grounded low-dimensional representations of fluid systems, standard Galerkin approaches often fail to produce physically consistent reduced turbulence closures.
In this work, we propose a hybrid surrogate modeling strategy that combines structure-preserving projection with data-driven learning. A discretize-then-project POD–Galerkin framework is employed to approximate velocity and pressure fields of the incompressible Navier–Stokes equations discretized via a finite-volume consistent flux method on collocated grids. To overcome the limitations of intrusive projection for turbulence modeling, the turbulent viscosity is instead reconstructed through a non-intrusive neural closure.
The mapping between the reduced velocity–pressure dynamics and the turbulent viscosity coefficients is learned using recurrent and attention-based neural architectures. A comparative study between Multilayer Perceptrons, Transformers, and Long Short-Term Memory networks shows that recurrent modeling significantly improves temporal stability and predictive accuracy in convection-dominated regimes.
Numerical experiments on a three-dimensional lid-driven cavity demonstrate that the proposed hybrid surrogate retains the physical consistency of projection-based ROMs while enhancing robustness in turbulent settings. The results illustrate how combining physics-based reduction with data-driven closure mechanisms can yield stable and accurate reduced-order surrogates for complex fluid systems.

Speaker: Kabir Bakhshaei (Sant’Anna School of Advanced Studies and University of Pisa)

12:45 Fast and Accurate Reconstruction of 3D Cardiac Displacement Fields from Sparse MRI-like Data via PBDW

Personalized cardiac diagnostics require accurate reconstruction of myocardial displacement fields from limited clinical imaging data. In this work, we propose an enhanced Parametrized-Background Data-Weak [1] framework for the recovery of 3D cardiac displacement fields from sparse, MRI-like observations, designed for fast and robust online application. The main contribution is the introduction of an $H$-size minibatch worst-orthogonal matching pursuit [2] strategy that accelerates sensor selection while maintaining reconstruction fidelity, together with memory optimizations that leverage block-matrix structures in vector-valued formulations to improve computational performance.

The methodology is assessed on a high-fidelity 3D left-ventricular model including simulated scar regions. Beginning with noise-free measurements, we gradually add Gaussian noise and increase spatial sparsity to mimic realistic MRI acquisition conditions. In noise-free settings, the proposed framework achieves a relative $L^2$-error of about 1e-5. Introducing Gaussian noise with a signal-to-noise ratio equals $10$, the relative $L^2$-error remains around 1e-2, and similar accuracy is obtained for sparse and noisy observation scenarios. Importantly, the online phase yields a speed-up of approximately four orders of magnitude compared to full finite element simulations, with reconstruction times below $0.1$ seconds.

These results indicate that the proposed strategy provides a computationally efficient and robst approach for reconstructing myocardial displacement fields from low-resolution sparse imaging data. Although further validation on clinical datasets and across a wider range of anatomical and pathological configurations is necessary, the current findings highlight its potential for integration into cardiac digital twinning workflows.

[1] Maday Y., Patera A. T., Penn J. D., Yano M., A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics, International Journal for Numerical Methods in Engineering, Vol. 102(5), pp. 933--965, 2014.
[2] Aretz N., Data assimilation and sensor selection for configurable forward models: challenges and opportunities for model order reduction methods, Dissertation, RWTH Aachen University, 2022.

Speaker: Francesco Mantegazza (University of Graz)

11:15 → 13:00 MS11.1 - Advances in Computational Plasticity, Damage and Fracture

11:15 A low-cost computational framework to identify Chaboche model parameters from biaxial loading conditions

The Chaboche kinematic hardening model provides reliable description of the cyclic-plastic behaviour of metals. However, the identification of Chaboche constants is a challenging task, which generally requires high computational cost and advanced optimization methods such as genetic algorithms, particle swarm optimization and differential evolution algorithms. Instead of using complex pointwise fitting operations, the global properties of the stabilized cycles, which are also of interest for further failure assessment, can be considered. For uniaxial cyclic-loadings, closed-form expressions can then be obtained to relate each Chaboche parameter to global properties of stabilized strain-controlled tests, such as hysteresis area, slope at the inversion points, stress range, plastic strain range and average points, and to ratcheting rate obtained from stress-controlled tests. Despite this and given the widespread use of the Chaboche model in modelling the cyclic-plastic behaviour of materials under multiaxial loading conditions, the identification of the parameters from non-uniaxial tests remain an open scientific question. This research aims to present a theoretical framework for the identification of Chaboche parameters by using the global properties of the stabilized cycles obtained through cyclic-torsional tests. In particular, this work demonstrates that low-cost mathematical expressions can be obtained even considering a biaxial loading case such as torsion. In addition, the proposed framework emphasizes that two strain-controlled tests, one symmetric ($R_{\gamma}=-1$) and one asymmetric ($R_{\gamma}\neq -1$), and one asymmetric moment-controlled test $R_\textup{M}\neq -1$ can be sufficient to identify all the parameters. These latter tests were then implemented considering thin-walled tubular specimens made of 42CrMo4, and the obtained results were compared with the corresponding ones extracted through classical uniaxial cyclic-tests. Finally, the contribution proposes mathematical expressions for further developments by using the Chaboche model to numerically describe combined torsional–tensile loadings.

Speaker: Lorenzo Romanelli (Department of Industrial Engineering, University of Trento)

11:30 Compression and three-point bending tests on polyethylene terephthalate tyre reinforcements

Polyethylene terephthalate (PET) textile multi-ply yarns, or cords, are widely employed in the automotive industry as reinforcement in rubber-based tyres to carry a significant part of the loads and maintain the overall shape [1]. They are typically obtained by twisting together multiple yarns, i.e., twisted bundles of flat filaments with a certain number of twists per meter.
In [2], a three-dimensional elastic-viscoplastic model for rayon cords, which couples the anisotropic behaviour of the single flat filament with its complex geometric orientation induced by the twisting, has been proposed and used to simulate monotonic and cyclic uniaxial tensile tests.
In this work, we present the results of the experimental campaign conducted in Pirelli Tyre laboratories according to ASTM standards, to characterize the mechanical behaviour of PET cords in confined compression and bending. Specifically, compression tests are performed on a cylindrical rubber specimen with an embedded cord, while the three-point bending tests are performed on strips of fabric made up of 10 warp PET cords with a thin weft of cotton yarns. Then, the model proposed in [2] is adapted to PET and employed to simulate the compression and three-point-bending tests. This allows the identification of material parameters in compression and assess the capability of the model to predict the mechanical response of PET cords.

[1] B. Rodgers, Tire Engineering: An introduction, CRC Press, 2020
[2] L. P. da Costa et al., Geometrical and Mechanical Modeling of Polymeric Multi-Ply Yarns. Applied sciences 14, 2024

Speaker: Emmanuel Denis Manoni (Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy)

11:45 Derivation of linear elasticity from energy functionals with infinitely many wells

We discuss the derivation of a linear elastic model starting from a nonlinear energy functional with infinitely many wells. Since the ground states of the elastic energy are unbounded, even a sequence of deformations with very small energy may still display very large deformation gradients and converge to a deformation with jumps. This may be interpreted as formation of plastic slips. We avoid such phenomenon by including a sufficiently large perturbation in terms of the second gradient, which penalises transitions from one well to another. In our analysis we employ a suitable weak convergence for deformation gradients excluding small subsets of the reference configuration, hence we may prove compactness by applying a rigidity estimate for incompatible fields.

Speaker: Giuliano Lazzaroni (Università di Firenze)

12:00 Remarks on Stability and Bifurcation in Irreversible Damage and Fracture

Abstract
What grants a theory its predictive power?

The numerical simulation of fracture in brittle materials poses fundamental challenges due to the non-convex and irreversible nature of the underlying variational models. Evolution problems governed by energetic principles may admit multiple equilibria, making the computed fracture path strongly dependent on algorithmic choices and stability criteria.
In this talk I share a series of remarks on the role of stability in the construction and computation of fracture evolution in gradient-damage models.
Considering a prototype brittle variational model with an irreversibility constraint, we analyse equilibrium states using the full second variation of the energy. Equilibrium maps obtained via branch-following reveal the coexistence of stable and unstable branches and show that quasi-Newton methods, relying on approximate Hessians, may miss bifurcation points and select non-physical paths.
To address these issues, I discuss a computational framework based on three nonlinear variational inequality solvers: a hybrid solver for constrained equilibrium, a bifurcation solver based on a projected Hessian spectrum, and a cone-constrained stability solver using a projection–scaling algorithm. Implemented in a modular Python framework built on DOLFINx, PETSc and SLEPc, these tools enable scalable PDE simulations and provide a general approach for detecting bifurcations, localisation and irreversible transitions in nonlinear systems.
This strategy provides a robust approach for tracking fracture paths in nonlinear damage models and clarifies the interplay between numerical algorithms, stability criteria, and the emergence of localisation and fracture patterns in brittle systems.

Speaker: Andrés A Leon Baldelli (Institut ∂'Alembert CNRS/Sorbonne)

12:15 (Cancelled) Interest of lattice rotation measurements around indentation to quantify slip-system interactions in FCC single crystal

This study targets a new observable for the simultaneous identification of the plastic parameters governing hardening mechanisms in Face Centered Cubic (FCC) single crystals via inverse method. Specifically, the goal is to design nanoindentation experiments that will be carried out to identify the 10 hardening parameters, including 7 slip system interaction parameters, of a single crystal Méric-Cailletaud type behavior law. The parameters are identified from lattice rotations after a Berkovich nanoindentation test, instead of classical observables such as the indentation curve (P-h) or residual topography.
In the literature, P–h curves have been widely used to identify elastic–plastic parameters of materials. However, many studies have shown that it is generally impossible to identify hardening plastic parameters using a single tip geometry. Residual topography provides richer information compared to P-h curve. However, previous works indicate that properly posing the inverse problem for parameter identification typically requires residual topography datasets collected from multiple relative orientations between tip and crystal.
The present work aims to quantify the information richness of the volumetric misorientation angle and the residual topography. Three-dimensional Crystal Plasticity finite element (CPFEM) simulation of the nano-indentation is performed for 13 selected crystallographic orientations. For each orientation, the information content of both the resulting volumetric misorientation angle field and residual topography is evaluated through a local parametric identifiability analysis.
The results demonstrate that the choice of observable strongly governs the achievable level of identifiability, while crystallographic orientation has a smaller, but noticeable, effect. In fact, the volumetric lattice misorientation angle field provides a better conditioning of the inverse problem than the residual topography. The identifiability analyses show that, when using the volumetric misorientation angle field as the observable, a single crystallographic orientation is sufficient to simultaneously identify the ten hardening parameters of a Méric–Cailletaud type law after Berkovich nanoindentation test.

Speaker: Jalal Smiri (Université Marie et Louis Pasteur, CNRS)

11:15 → 13:00 MS20 - Synchronization Dynamics, Collective Behaviors and Nonlinear Mechanics

11:15 Nonlinear Pulse Propagation in Arrays of Bistable Tensegrity Prisms

The study explores impact-induced nonlinear wave phenomena in one-dimensional assemblies of bistable tensegrity prisms. Each unit cell consists of an all-bar prism characterized by a two-well axial equilibrium path—either strain-softening or strain-hardening—periodically coupled with concentrated masses. Finite-chain numerical analyses are conducted to characterize the initiation, evolution, and dissipation of axial strain disturbances.
Systems built from stockier prism elements exhibit a softening bistable constitutive response, generating compressive wavefronts followed by dispersive oscillatory trails and gradual amplitude decay. Conversely, configurations employing more slender prisms display a hardening bistable response and sustain highly localized compression pulses with only minor accompanying oscillations.
In contrast to conventional bistable mass–spring lattices, the tensegrity architectures examined here inherently couple longitudinal deformation with torsional kinematics. Despite such geometric nonlinearity, the computed impact responses show strong qualitative consistency with established findings on solitary-wave propagation in bistable discrete chains. The peculiar dynamic features emerging in bistable tensegrity lattices suggest promising opportunities for tailored energy steering, pulse manipulation, and spatial confinement of mechanical disturbances.

Speaker: Rana Nazifi Charandabi (University of Salerno)

11:30 Reduced-order representations of friction-induced nonlinear dynamics in multi-degree-of-freedom systems

Dry friction is commonly present in mechanical structures through joints and interfaces, introducing nonlinear phenomena such as stick–slip transitions and partial locking. While friction is often regarded as a source of damping, recent studies have shown that it can significantly influence vibration-based damage detection, sometimes enhancing damage signatures and sometimes masking them.

Recent research has also explored data-driven strategies to cope with the limited availability of labeled data in structural health monitoring. In particular, nonlinear structural behavior can be exploited to generate richer datasets through multi-excitation testing procedures, enabling physics-informed data augmentation for deep-learning-based fault diagnosis.

Despite these advances, the physical mechanisms by which frictional nonlinearities modify the observability of structural damage signatures are still not fully understood. Experimental investigations on multi-degree-of-freedom systems have shown that increasing the excitation level may either amplify or suppress the spectral signatures associated with structural defects.

This work proposes a complementary interpretation of these phenomena based on a reduced-order dynamic representation of the structure. In particular, the response of the system under different friction regimes is analyzed in terms of dominant modal subspaces and equivalent low-order models. Within this framework, friction-induced fully stuck configurations can be interpreted as a projection of the system dynamics onto reduced modal spaces, which may alter the observability of damage-related features in the frequency response.

The proposed perspective is illustrated through vibration tests performed on a railway pantograph structure, characterized by multiple frictional joints and complex modal interactions. The results provide insight into the mechanisms through which friction modifies the detectability of structural damage and suggest possible directions for improving vibration-based structural health monitoring techniques in nonlinear mechanical systems.

SANTAMATO, Giancarlo, et al. Leveraging systems’ non-linearity to tackle the scarcity of data in the design of intelligent fault diagnosis systems. Nonlinear Dynamics, 2024, 112.18: 16153-16166.

Speaker: Giancarlo Santamato (Scuola Superiore Sant'Anna)

11:45 Coupling flutter instability and electromagnetic interactions in a “virtual” microrobotics experiment

Bio-inspired microrobots are widely investigated as controllable devices for swimming in aqueous environments since their trajectories can be guided via the use of Lorentz-type forces [1]. Yet, the effectiveness of the electromagnetic interaction depends strongly on the locomotion mechanism [2] of the device. At low Reynolds numbers, some propulsion strategies are characterized by flutter instability [3], thereby inducing self-sustained oscillations in certain “rod-shaped” portions of the robots. In this presentation we focus on two “virtual” experiments involving a fluttering microrobot interacting with an ideal solenoid [4]. Our goal is to assess the impact of the electromagnetic interaction on the robot’s fluttering behavior, showing, in the process, how certain effects proper of electromagnetism can be “rediscovered” also in experiments conceived for microrobotics [5]. The design of the robot is inspired by a variant of Ziegler’s double pendulum analyzed in [6].

Acknowledgements: Financial support from ERC-ADG-2021-101052956-BEYOND

References
[1] Shen, H., Cai, S., Wang, Z., Ge, Z., Yang, W., “Magnetically driven microrobots: Recent progress and future development”, Materials & Design, 227, 111735 (2023).
[2] Zhang, L., Peyer, K. E., Nelson, B. J., “Artificial bacterial flagella: Fabrication and magnetic control”, Nano Letters, 9, 3663–3667 (2009).
[3] Dreyfus, R., Baudry, J., Roper, M.L., Fermigier, M., Stone, H.A., Bibette, J.: “Microscopic artificial swimmers”, Nature, 437, 862—865 (2005).
[4] Pastore, A., Harrop, J.C., Bigoni, D., Grillo, A., “Dynamics of a charged Ziegler’s double pendulum under the joint action of a follower force and Lorentz force”, (2026) Submitted.
[5] Rousseaux, G., Kofman, R., Minazzoli, O., “The Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theory”, Eur. Phys. J. D, 49, 249–256, (2008).
[6] Cazzolli, A., Dal Corso, F., Bigoni, D., “Non-holonomic constraints inducing flutter instability in structures under conservative loadings”, J. Mech. Phys. Solids, 138, 103919 (2020).

Speaker: Andrea Pastore (Politecnico di Torino)

12:15 Thermo-Mechanical Instabilities in Snow Slabs Avalanches: An Ab-Initio Quantized Fracture Thermo-Mechanics (QFTM) Approach

Climate change is significantly affecting mountain environments, with increasing temperatures altering snowpack stability and potentially increasing the frequency of snow-slab avalanches. Understanding how temperature influences avalanche triggering is therefore crucial for assessing the impact of warming climates on snow hazards. Although field observations consistently indicate that temperature plays a key role in avalanche release, a rigorous analytical framework capable of quantitatively describing this influence is still lacking.
In this work, we develop a theoretical framework to investigate the thermo-mechanical mechanisms governing avalanche triggering. The model builds upon recent papers in which the classical Griffith energy balance for fracture has been extended to account for coupled thermo-mechanical loading conditions. While those studies primarily addressed Mode I fracture, here we focus on Mode II (shear) fracture, which more accurately represents the failure of the weak snow layer responsible for slab detachment.
The formulation explicitly incorporates finite slab dimensions and friction. Starting from an ab-initio discrete description, the model consistently recovers classical continuum fracture mechanics results in the appropriate limiting case. Interestingly, applying the Quantized Fracture Mechanics framework to the continuum formulation leads back to the discrete model, highlighting the interplay between discrete and continuum descriptions in fracture processes.
Within this energetic perspective, snowpack stability emerges from the nonlinear competition between elastic deformation energy, external loading, fracture energy, frictional dissipation, and entropic contributions associated with thermal fluctuations. Avalanche release can therefore be interpreted as a thermo-mechanical instability arising from thermo-mechanical interactions within the snowpack.
The analysis predicts a temperature-dependent critical load for weak-layer failure that decreases with increasing temperature according to the scaling law $(1-T/T_c)^{1/2}$, where the critical temperature $T_c$ depends on the system’s parameters.
These results provide a quantitative framework linking temperature variations to snowpack stability and establish a direct theoretical connection between climate warming and the increased likelihood of avalanche triggering.

Speaker: Claudia Binetti (University of Trento)

12:30 Inelastic effective properties of bone-like tissue via Asymptotic Homogenization

Cortical bone is an example of a multiscale biological tissue, being characterized by a sharp separation between the macroscopic lenght scale, at which the cortical bone appears like a continuum with defined structural biological functionality, and the microscopic length scale, at which it is possible to identify an elementary unit, i.e. the lamella, that, when repeated, composes the tissue. Hence, the macroscopic mechanical behaviour of the cortical bone depends on the resolution of microscopic processes such as remodeling, but also the converse is true. In particular, we study the reorganization of the bone’s inner structure that leads to the formation of “plastic zones”, which are diffuse plastic interfaces covering multiple lamellae [1].
In our work, we put forward a general framework for studying the mechanics of a composite medium, made of two solids constituents, both of which can incur remodelling, and that present a microscale characterized by a unitary cell of arbitrary shape. In order to study the formation of a diffuse interface, we adapt Gurtin&Anand theory of strain-gradient plasticity [2] to this biological setting. Under the hypothesis of well-separation of the geometrical scales, we employ the techniques of Asymptotic Homogenization to derive the homogenized response of the system in the form of effective coefficients embedding the microscopic structural information. Lastly, we perform some numerical simulations on a simplified geometrical setting to provide an evaluation of the strain gradient remodeling effects [3].

References:
[1] D. M. Robertson, D. Robertson, C. R. Barrett, Journal of Biomechanics, Elsevier BV, 1978.
[2] M. E. Gurtin, L. Anand, International Journal of Plasticity, Elsevier BV, 2005.
[3] A. Giammarini, A. Ramírez-Torres, A. Grillo, Math. Methods in the App. Sciences, Wiley, 2024.

Speaker: Alessandro Giammarini (Politecnico di Milano)

13:00 → 14:00 Lunch break

14:00 → 15:15 MS10 - Data Assimilation and Uncertainty Quantification for Complex Flows

14:00 Scale-Adaptive Simulation with Adaptive Mesh Refinement for a digital twin framework

Adaptive mesh refinement (AMR) offers a practical route toward digital twins in computational fluid dynamics, automatically tailoring mesh resolution for each full-order simulation to maintain accuracy across large ensembles with varying boundary conditions and geometries. This work investigates the coupling of Scale-Adaptive Unsteady Reynolds-Averaged Navier-Stokes (SA-URANS) modelling with AMR to improve the trade-off between computational cost and predictive accuracy in turbulent flow simulations, and evaluates the proposed methodology on canonical urban microclimate configurations. Turbulence-driven refinement strategies are implemented in OpenFOAM v13 through extensions of the dynamic-mesh infrastructure, with refinement indicator fields computed on the fly during simulations. In addition to a conventional Q-criterion-based strategy, novel criteria based on the von Kármán length scale are introduced to concentrate resolution where scale-resolving behaviour is expected. The results indicate that turbulence-driven AMR enables simulations to begin from a coarse, far-from-optimal computational grid and progressively increase effective resolution under fixed resource constraints. This provides a flexible, automation-compatible framework that supports the use of SA-URANS with AMR as a scalable building block for digital twins.

Speaker: Pietro Tavazzi (Sant'Anna School of advanced studies)

14:15 Coupled flow-mechanics for Uncertainty Quantification and Parameter estimation in Subsurface Resource Exploitation

Groundwater and other subsurface resources play a fundamental role in modern water and energy systems, yet their exploitation can induce significant geomechanical responses such as land subsidence. In aquifer systems, overexploitation—defined as extraction rates exceeding natural recharge—can lead to substantial declines in piezometric levels, compaction of aquifer deposits, reduction of porosity and storage capacity, and progressive land subsidence. These processes may compromise soil stability, threaten infrastructures, and reduce hydraulic safety. Physically based geomechanical models provide an effective framework for simulating the coupled processes governing subsurface fluid flow and deformation. However, their predictive reliability is strongly affected by uncertainties in the parameterization of constitutive models describing the hydraulic and mechanical behavior of geological formations. In this work, we present an integrated modeling framework combining physically based poromechanical simulations with uncertainty quantification, sensitivity analysis, and data assimilation techniques to improve the characterization and predictive capability of subsurface systems.
The approach relies on three-dimensional fluid–poromechanical models that simulate the interaction between groundwater flow and subsurface deformation through explicit representation of porosity changes. Aquifer and reservoir properties, including hydraulic conductivity and compressibility, are constrained using multiple observational datasets, such as piezometric measurements and satellite-based surface displacement (InSAR). Parameter estimation and uncertainty reduction are performed within a Bayesian framework, integrating inversion techniques with ensemble-based data assimilation methods. To overcome the high computational cost associated with repeated simulations of nonlinear geomechanical models, surrogate modeling techniques are introduced. Sparse-grid approximations and generalized Polynomial Chaos Expansion are employed to approximate the forward model response, reducing the computational burden of Bayesian inversion and data assimilation. Applications to both a synthetic deep hydrocarbon reservoir and the Alto Guadalentín aquifer system (Spain) demonstrate that integrating satellite deformation data substantially improves the characterization of subsurface properties and enhances the robustness of geomechanical predictions while maintaining computational efficiency.

Speaker: Claudia Zoccarato (Universita' degli Studi di Padova)

14:30 Data-Driven Correction of RANS Models for Urban Flow Prediction via Machine Learning and Data Assimilation

Despite their computational efficiency, Reynolds-Averaged Navier-Stokes (RANS) models often struggle to accurately represent the complex turbulence and flow separation typical of urban environments.
These limitations highlight the need for data-driven correction strategies to improve predictive accuracy.
Enhancing RANS performance is essential for aerodynamic load estimation and for evaluating pedestrian comfort and pollutant dispersion, critical aspects of urban planning and environmental design.
This work presents a machine learning framework for analyzing urban flows, grounded in a prior
data assimilation phase. The study focuses on the Architectural Institute of Japan (AIJ) [1] Case A
dataset, which models flow around a single rectangular building at varying heights (see Fig. 1) under
controlled inlet conditions reproducing the atmospheric boundary layer. Experimental measurements of
velocity and turbulent kinetic energy are available for validation. Baseline steady RANS simulations are
performed in OpenFOAM using the k − ε turbulence model, incorporating the atmospheric boundary
layer profile. The results of this model show discrepancies with experimental data (see Fig. 1).
The same procedure previously applied to rectangular cylinders [2] will be used herein for this
more complex three dimensional case. To perform the data assimilation, the DAFoam library, written
for OpenFOAM, is employed. In this phase field variables extracted from scale-resolving simulations
are utilized to compute correction fields to enhance the accuracy of the k − ε baseline model. More
specifically, an objective functional is chosen to minimize the discrepancy in both the velocity field
within a region around the body and the pressure field on the body’s surface. The corrective fields
obtained for different building heights are used to train a machine learning regression model to predict
the correction terms of the RANS baseline model for unseen configurations, for instance varying the
building heigth or wind intensity and direction.

Speaker: Aurora Ursetto

14:45 A bi-fidelity sparse-grid interpolation for Uncertainty Quantification and Sensitivity Analysis of complex flows

High-fidelity computational models of complex flows provide accurate predictions, but their significant computational cost often makes them impractical for applications requiring repeated evaluations, such as uncertainty quantification, optimization, or the generation of databases for machine-learning training. Surrogate modeling addresses this issue by approximating the mapping between input parameters and output responses when direct high-fidelity evaluations are too expensive. Stochastic collocation methods are a common example. However, when the number of uncertain parameters increases, the computational cost of standard tensor-product collocation grows exponentially. Sparse grids, originally introduced by Smolyak in 1963, alleviate this curse of dimensionality compared to full tensor grids, but they treat all regions of the parameter space isotropically, which can be inefficient when higher resolution is required only in specific regions.

This work presents a bi-fidelity framework for constructing sparse grid interpolants guided by an error indicator that provides a zero-cost estimate of the hierarchical surplus. The indicator is evaluated at candidate points in the next-level grid $w+1$ not already included in the base grid $w$, by computing the relative difference between the predictions of two consecutive interpolants of level $w$ and $w-1$. Candidate points are ranked according to this metric and only the most impactful ones are selected up to a prescribed budget. The final higher-order model is then built by evaluating the expensive objective function only at these selected points, while the remaining nodes of the $w+1$ grid are assigned the values predicted by the level-$w$ surrogate. The approach is tested on analytical functions and on the sensitivity analysis of flashback in hydrogen-fueled perforated burners with respect to four geometrical parameters. Results show that the proposed framework significantly reduces the error while requiring far fewer DNS evaluations than a fully resolved higher-level sparse grid.

Speaker: Filippo Fruzza (University of Pisa)

15:00 Uncertainty Quantification of High-Order Spectral Methods for Extreme Wave Prediction

Rogue waves are extreme manifestations of ocean dynamics, whose prediction is strongly affected by uncertainty in the characterization of sea states. This work develops and applies advanced Uncertainty Quantification (UQ) methodologies for the probabilistic assessment of extreme wave occurrence in nonlinear irregular seas. Sea states are described through parametric spectral models, whose defining parameters (e.g. directional spreading, wave steepness, peak enhancement factor) are treated as uncertain inputs. A non-intrusive UQ framework based on adaptive sparse grids and stochastic collocation methods is employed to propagate these uncertainties through a high-fidelity phase-resolving solver. Deterministic simulations rely on a High-Order Spectral formulation for deep-water gravity waves, that solves the time evolution of the free surface height on a periodic domain, considering non-linear interactions and dissipation due to wave breaking. In order to enhance local surrogate accuracy while limiting computational cost, an informed adaptive refinement strategy is introduced. The approach exploits the hierarchical structure of sparse grids by estimating the local discrepancy between interpolants constructed at consecutive levels. Rather than upgrading the full grid level, only nodes exceeding a dynamically defined relative-error threshold are selected for additional high-fidelity simulations. This targeted refinement enables the mitigation of local interpolation anomalies and improves convergence in critical parametric regions, while avoiding the prohibitive cost of a full-level refinement. The proposed framework facilitates the operational deployment of phase-resolving models and integrates them with phase-averaged approaches. This integration enables rapid, uncertainty-aware prediction of extreme wave statistics in realistic marine environments.

Speaker: Andrea Giorgi (Università di Pisa)

14:00 → 15:15 MS11.2 - Advances in Computational Plasticity, Damage and Fracture

14:00 (Cancelled) Fracture of high-strength aluminum sheet in single point incremental forming

Single Point Incremental Forming (SPIF) is an innovative forming technique in which a stylus forming tool incrementally deforms a blank sheet into the final shape. The deformation mechanism is quite different compared to traditional forming processes. Moreover, fracture prediction remains a significant challenge. In the current study, a hybrid experimental–numerical approach was conducted to calibrate the Johnson–Cook damage model for a high-strength aluminum alloy. The calibrated model serves as a sophisticated tool for capturing the onset of fracture in SPIF. Both isotropic and anisotropic material behaviors were investigated. The results indicate that the anisotropic model is capable of predicting fracture in terms of location and depth with a relative error of $7.74\%$ compared to the experimental results.

Speaker: Marwen Habbachi (University of Miskolc)

14:15 Path-following methods for quasi-static crack propagation : Application to phase-field fracture

Numerical simulations of quasi-static crack propagation in brittle materials often suffer from numerical instabilities, such as snapback events, due to structural softening.
In variational phase-field fracture models, these instabilities manifest as abrupt crack jumps, thereby impeding physical validity, as the energy minimization is performed over a significant crack increment.
Moreover, they often prevent incremental force boundary conditions, as they may lead to a loss of force balance as soon as the crack starts propagating.

This study introduces path-following methods to mitigate such instabilities in quasi-static phase-field fracture simulations.
We evaluate existing methods alongside a novel approach, Control by Maximum Strain Increment Outside the Crack (CMSIOC), which enforces stable crack growth by constraining strain increments in the uncracked region.
All studied methods rely on a single scalar control equation that depends solely on displacement fields, enabling integration into classical staggered solvers without major changes.

Performance is assessed via three benchmark problems of increasing complexity, with results compared against Linear Elastic Fracture Mechanics (LEFM) references based on Griffith's criterion and the $G$-max criterion.
Our findings show that CMSIOC:

1. Accurately follows the equilibrium path, avoiding abrupt crack jumps while preserving physical validity;
2. Supports force-controlled boundary conditions without loss of force balance during propagation;
3. Ensures uniform incremental crack growth, properly distributing the computational efforts across load steps.

These results highlight CMSIOC's robustness as a model- and problem-independent solution for stable phase-field fracture simulations.

Speaker: Flavien Loiseau (IMSIA (ENSTA, EdF, IP Paris, CNRS))

14:30 Variational approach to dynamic cohesive fractures

Variational approach to dynamic cohesive fractures

key words : variational methods, phase-field models, cohesive fracture, damage-plasticity models, dynamics

Gradient damage models (aka phase-field models) are widely used to predict the nucleation and propagation of cracks. Recently, a novel class of phase-field models based on coupled damage-plasticity models have been developed. Their capabilities to predict the nucleation and propagation of cracks in brittle and ductile materials under complex stress states has been validated in a quasi-static regime.
When the load varies slowly with time, the quasistatic approach is preferred to the dynamic approach for its simplicity. However, when that is not the case, one important challenge is to extend these models in a dynamical setting.

In this work, we present a variational approach to model the dynamics of cohesive fractures. In particular, we show some analytical and numerical results of such approach by studying the behavior of a homogeneous one-dimensional bar. At difference with respect to the quasi-static case, the variational approach no longer uses the energetic stability criterion, but is formulated in terms of the principle of least action. A Lagrangian is thus defined and given by the difference between the potential energy and kinetic energy of the body. Irreversibility and energy balance, as in the quasi-static case, are then used to complete the variational formulation of the problem.

Preliminary results obtained in the antiplane case suggest that this approach can potentially unify within a single consistent variational theory key concepts developed to predict or prevent material failure: Griffith and cohesive crack models, damage models, plasticity, strength criteria, and limit analysis. This work would contribute in this direction by extending the framework to include dynamical problems.

Speaker: Giovanni Rizzo (Institut Jean Le Rond d’Alembert, Sorbonne Université & Università di Pisa)

14:45 Numerical Benchmarking of Phase-Field Fracture Implementations Across Open-Source and Commercial Finite Element Frameworks

Phase-field models for brittle fracture have become a widely adopted tool for simulating crack initiation and propagation without explicit tracking algorithms. As their popularity has grown, so has the variety of available implementation strategies, encompassing different solvers, coupling schemes, irreversibility treatments, and software platforms. While each approach has been individually validated in the literature, direct and systematic comparisons remain scarce, leaving practitioners without clear guidance on which strategy best suits their specific problem in terms of accuracy, robustness, and computational cost.
This work addresses this gap through a comprehensive cross-framework benchmarking campaign for the AT2 phase-field fracture model, implemented in the open-source library FEniCSx and the commercial solver Abaqus. In the work, a progressive suite of benchmark problems is proposed to expose the practical strengths and limitations of each approach under controlled conditions. In FEniCSx, the history-variable method is contrasted against bound-constrained variational inequality solvers. In Abaqus, monolithic and staggered coupling schemes are evaluated through a heat-transfer analogy for the implicit solver.
The results reveal that while all strategies converge to framework-independent solutions when properly configured, they differ substantially in iteration count, time-step sensitivity, and robustness during crack propagation. These findings could help researchers and engineers selecting the most reliable numerical tool for their phase-field fracture analyses.

Speaker: Stefano Domesi (Sapienza University of Rome)

15:00 (Cancelled) Modeling the Creep Behavior of Cracked Concrete Beams Strengthened with Externally Bonded FRP Plates Using a Cohesive Zone Approach

This study presents a creep response model to investigate the long-term behavior of interfacial shear stresses induced by intermediate flexural cracks in reinforced concrete beams strengthened with externally bonded fiber-reinforced polymer (FRP) plates. A theoretical framework based on a bi-linear cohesive zone model is developed to describe intermediate crack-induced debonding. The proposed approach integrates both the initiation and propagation of debonding through time increments. The creep behavior of the RC beam, adhesive layer, and FRP plate is incorporated by considering the time-dependent mechanical properties of each component. The resulting time-dependent stress–deformation relationship caused by creep is described through a bond-slip law. Based on this concept, a new interfacial law is proposed that accounts for the time-dependent properties of all constituents of the strengthened beam system (concrete-FRP-interface). In the formulation, the total energy at the interface is assumed to remain constant during the creep response associated with intermediate cracking. The predictions obtained from the proposed model show good agreement with results reported in the literature, confirming its capability to capture the long-term interfacial behavior of FRP-strengthened RC beams. In addition, a parametric study is conducted to evaluate the influence of mechanical properties and thickness variations of the FRP plate, concrete substrate, and adhesive layer on interfacial debonding. The results indicate that creep significantly accelerates the debonding process over time. The softening zone develops rapidly, and the load-carrying capacity of the strengthened beam is progressively affected as time increases.

Speaker: Khamis Hadjazi (Composite Structures and Innovative Materials Laboratory (LSCMI), Faculty of Mechanic Engineering, University of Science and Technology of Oran (USTO), Oran)

14:00 → 15:15 MS19 - Optimization Methods in Structural Mechanics: Numerical Models and Applications

14:00 Optimization-based non-smooth contact dynamics of curved rigid bodies

Non-Smooth Contact Dynamics (NSCD) is a well-established method for the dynamic analysis of rigid bodies and has recently been extended to historical masonry structures, where the arrangement of units has a strong influence on the global response. While most of the existing formulations assume prismatic block geometries, several historical structures are composed of elements with curved shapes (for instance, arches and vaults), for which the accurate representation of geometry is fundamental.
In this contribution, a NSCD-based computational strategy is proposed in which curved rigid blocks are described using a NURBS-based geometric formulation (where NURBS denotes Non-Uniform Rational B-Spline). Each block is modelled as a closed solid defined by NURBS boundary surfaces, providing the exact representation of geometry and accurate determination of inertial properties via surface integration. The dynamic response of the system is governed by the impulse–momentum balance at the block level, where external actions and contact interactions induce variations in the velocity field over the discrete time steps. Normal and tangential contact impulses are introduced at block interfaces and governed by a frictional contact law. The contact detection between curved bodies is carried out by combining the Gilbert-Johnson-Keerthi (GJK) distance algorithm with a point-inversion procedure conceived for NURBS surfaces. At each time increment, the resulting non-smooth dynamic problem is written as a second-order conic programming (SOCP) problem, whose solution provides the admissible block velocities with respect to contact and frictional constraints.
The proposed formulations highlight the link between structural dynamics, convex optimization, and geometry. This approach seems particularly suited for analysis of the responses of historical masonry structures to dynamic actions.

Speaker: Nicola Grillanda (Department of Architecture, University of Ferrara)

14:15 Onset of yielding in imperfect lattice structures: an Upper-Bound Limit Analysis framework

Lattice structures are widespread in natural systems at the microscopic scale and are increasingly adopted in engineering applications at multiple scales due to their high strength-to-weight ratio and energy absorption capacity. The reliable assessment of their load-bearing capacity is therefore essential for safe design and must account for both geometrical and mechanical imperfections arising from natural variability or manufacturing processes.

In this contribution, the collapse strength of imperfect planar lattice structures is evaluated within an upper-bound limit analysis framework formulated as a limit programming problem. The failure load is obtained by solving a constrained optimisation problem in which kinematically admissible collapse mechanisms are imposed through linear programming. This approach provides an efficient alternative to nonlinear incremental micro-mechanical analyses, which become computationally demanding for large lattice systems.

Geometrical imperfections are introduced by perturbing the periodic cell configuration, thus affecting cell shape, while mechanical imperfections are modelled as random variations of material properties. Both randomly distributed and localised defects are considered. A Monte Carlo simulation strategy is coupled with the optimisation-based limit formulation to quantify the influence of imperfection intensity and relative density on the collapse load. The structural strength is characterised in terms of statistical moments and probability density functions.

Results show that the sensitivity to defects depends on the lattice geometry. Imperfections not only reduce the collapse load but also alter the governing failure mechanisms. The proposed optimisation-based upper-bound framework proves to be an effective and robust tool for the systematic assessment of strength variability in imperfect lattice structures.

Speaker: Mattia Schiantella (University of Perugia)

14:30 On multistable beam-lattice structures

Interest in beam-lattice metamaterials is growing nowadays. They mimic classic crystalline lattices and exhibit promising properties, including low weight, enhanced flexibility, and efficient energy absorption. In the analysis of beam-lattice metamaterials, instabilities analogous to the classical Euler instability are often anticipated. For instance, in elastomeric open-cell foams, such instabilities manifest as a plateau in the microscale force-displacement response, which resembles plastic behaviour.
The objective of this lecture is to examine multistable structures, defined as systems possessing multiple equilibrium states under a specified external force. These structures are known to display intricate snap-through and snap-back phenomena. As a representative example, a periodic truss system constructed from elementary cells analogous to the von Mises truss will be analyzed. Equilibrium equations have been derived for select configurations, and the corresponding equilibrium paths are presented. Despite their nominal simplicity, these systems may exhibit complex mechanical responses, with equilibrium paths characterized by multiple loops and branches. Parametric analyses will also be discussed.
Finally, further modeling of these structures is undertaken utilizing effective medium approaches that account for material instabilities.

Speaker: Matteo Lai (Università degli Studi di Cagliari)

14:45 Optimal vibration control in structures equipped with Active Mass Dampers

Active vibration control through Active Mass Dampers (AMDs) represents an effective and increasingly widespread strategy for reducing the dynamic response of civil structures subjected to actions such as wind, earthquakes, and other induced dynamic loads, both in the design phase of new buildings and in the retrofit of existing structures.
However, the performance of such systems does not depend solely on the adopted control law; it is also strongly influenced by the placement of the actuators within the structure. In this context, the present study addresses the problem of optimizing the placement of AMDs through the use of Genetic Algorithms (GAs), with the aim of maximizing vibration mitigation effectiveness.
The developed methodology integrates a non-classical numerical structural model (capable of accounting for the contribution of concentrated damping) with an evolutionary optimization procedure. The analysis is carried out using numerical models of the structure coupled with the AMDs and time-domain simulations based on modal superposition, in order to assess the influence of different placement configurations on the overall performance of the controlled system. Different formulations of the optimization problem are considered and compared, based on modal criteria, dynamic response indicators, and multi-objective functions, analyzing the impact of the various parameters to be maximized or minimized.
The results obtained from representative case studies show that evolutionary optimization makes it possible to identify non-intuitive yet highly effective placements, achieving significant reductions in floor accelerations and improvements in structural comfort and safety.
This work also highlights the flexibility of the method in retrofit interventions, where architectural and structural constraints impose limited design choices. The integration of dynamic modeling and evolutionary optimization thus proves to be an effective tool for supporting designers in defining active control strategies, contributing to the development of intelligent and adaptive solutions for dynamic risk mitigation in existing constructions.

Speaker: Nicola Grillanda (Department of Architecture, University of Ferrara)

15:15 → 15:30 Closing remarks