Speaker
Description
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.