GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems

TL;DR

GFINNs are neural networks designed with a physics-informed architecture based on the GENERIC formalism, capable of accurately modeling both deterministic and stochastic dynamical systems, outperforming existing methods.

Contribution

This paper introduces GFINNs, a novel neural network architecture that incorporates the GENERIC formalism's conditions, providing a flexible and expressive framework for physics-informed learning.

Findings

GFINNs successfully model complex physical systems with high accuracy.

They outperform existing methods in multiple simulation benchmarks.

Theoretical proof of universal approximation capability.

Abstract

We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. We demonstrate the performance of GFINNs in three simulation problems: gas containers exchanging heat and volume, thermoelastic double pendulum and the Langevin dynamics. In all the examples, GFINNs outperform existing methods, hence demonstrating good accuracy in predictions for both deterministic and stochastic systems.