Abstract

Non-equilibrium phenomena are ubiquitous across material systems and of great technological relevance. Examples of such phenomena include diffusion processes in liquid and gases, viscoelasticity and plasticity in solids, and rheological behavior of colloidal and granular media. Despite their ubiquity and importance, the understanding of non-equilibrium phenomena remains in its infancy compared with classical equilibrium thermodynamics and statistical mechanics from both theoretical and computational aspects. As a consequence, current modeling and simulation strategies, including multiscale paradigms, are mostly trapped within a compromise between computational efficiency and physical fidelity.

In this talk, I present a data-driven framework for constitutive modeling of non-equilibrium systems that integrates continuum mechanics, statistical physics, and machine learning. The first part introduces a machine learning architecture called Variational Onsager Neural Networks (VONNs) to learn thermodynamically consistent non-equilibrium evolution PDEs from macroscopic material responses. The second part focuses on Statistical-Physics-Informed Neural Networks (Stat-PINNs), a multiscale learning framework for inferring coarse-grained dissipative evolution equations from stochastic particle dynamics by leveraging that fluctuation-dissipation relations. Together, these approaches provide a physically grounded and computationally efficient pathway for learning constitutive laws of non-equilibrium systems across scales.