Nonlinear GENERIC Informed Neural Networks (N-GINNs): learning GENERIC dynamics with non-quadratic dissipation potentials

TL;DR

This paper presents N-GINNs, a deep learning framework that discovers thermodynamically consistent evolution equations for systems with coupled conservative and dissipative dynamics, including non-quadratic dissipation potentials.

Contribution

The authors introduce N-GINNs, which incorporate generalized gradient flows and enforce thermodynamic laws, broadening the class of systems that can be learned from data.

Findings

Successfully inferred models for a harmonic oscillator coupled to a heat bath.

Accurately modeled an idealized chemical motor with thermodynamic consistency.

Demonstrated the method on a viscoplastic Perzyna-type model with nonlinear dissipation.

Abstract

We introduce Nonlinear GENERIC Informed Neural Networks (N-GINNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium Reversible-Irreversible Coupling). Such systems exhibit coupled conservative and dissipative dynamics, and can be described via the superposition of a Hamiltonian flow and a generalized gradient flow. In contrast to existing approaches, our formulation incorporates generalized gradient flows via convex dissipation potentials, enabling the identification of a broader class of thermodynamically consistent dynamics, including systems with non-quadratic dissipation potentials. Thermodynamic structure is strongly enforced by construction through suitable reparameterizations of both the bivector operator and the dissipation potential, ensuring exact compliance with the first and second laws of thermodynamics. We validate the proposed approach on three representative examples: a harmonic oscillator coupled to a heat bath, an idealized chemical motor, and a one-dimensional viscoplastic model of Perzyna type. These results demonstrate the method's ability to accurately infer thermodynamically consistent models from data for systems incorporating both conservative and nonlinear dissipative dynamics.