Nonlinear GENERIC Informed Neural Networks (N-GINNs): learning GENERIC dynamics with non-quadratic dissipation potentials
For researchers modeling complex physical systems, this work provides a method to learn thermodynamically consistent dynamics from data, extending prior approaches to handle non-quadratic dissipation potentials.
The paper introduces N-GINNs, a deep learning framework that learns evolution equations for systems with coupled conservative and dissipative dynamics by enforcing the nonlinear GENERIC formalism, including non-quadratic dissipation potentials. The method is validated on three examples, demonstrating accurate inference of thermodynamically consistent models from data.
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.