Thermodynamics-informed graph neural networks

TL;DR

This paper introduces a deep learning approach combining graph neural networks and thermodynamic principles to accurately predict the evolution of dissipative systems, enhancing generalization and modeling non-conservative dynamics.

Contribution

It presents a novel thermodynamics-informed graph neural network method that incorporates geometric and thermodynamic biases for modeling complex dissipative systems.

Findings

Achieved less than 3% relative mean error across multiple fluid and solid mechanics examples.

Demonstrated the effectiveness of combining GNNs with GENERIC thermodynamic structure.

Provided ablation studies validating the approach's components.

Abstract

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior with permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively, achieving relative mean errors of less than 3% in all the tested examples. Two ablation studies are provided based on recent works in both physics-informed and geometric deep learning.