GIMC SIMAI Young 2026

Session

MS07.1 - Recent Advances in Data-Driven Surrogate Modeling

5 Jun 2026, 09:00

Pisa

112. Learning adaptive basis representations for parametrized PDEs with Deep Orthogonal Decomposition

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

05/06/2026, 09:00

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

82. Benchmarking the translation invariance of Neural Operators for the FitzHugh-Nagumo model

Luca Pellegrini (University of Pavia)

05/06/2026, 09:15

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

90. Learning the continuous-time dynamics: from trajectories to velocities

Nicola Farenga (Politecnico di Milano)

05/06/2026, 09:30

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

18. Randomized Low-Rank Natural Gradient Methods for Scalable Neural PDE Learning

Ivan Bioli (Università di Pavia)

05/06/2026, 09:45

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

69. Separable Representations of Optimal Value Functions via Neural Networks

Luca Saluzzi (Università degli studi di Ferrara)

05/06/2026, 10:00

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

46. Step-by-Step Time-Discrete PINNs: Embedding Time Integrators into Neural Networks

Carmine Valentino (University of Salerno)

05/06/2026, 10:15

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...

138. Space-time continuous pde forecasting using equivariant neural fields

Riccardo Valperga (AI4I)

05/06/2026, 10:30

MS07 - Recent Advances in Data-Driven Surrogate Modeling

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...