Thermodynamics-Informed Graph Neural Networks

In this article, 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 nonconservative 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. Impact Statement Distilling physical laws from data, either in symbolic form or numeric form, is a problem of utmost importance in the field of Artificial Intelligence. Many different attempts have been developed in recent times based on supervised procedures and different types of neural networks or other more classical regression techniques. In our approach, the scientific knowledge of the physics governing the problem is very important, and is imposed by using the most general formulation: Thermodynamics (often referred as the physics of physics). Furthermore, the use of geometric deep learning enables our method to handle unstructured meshed domains, improving its generalizability. With a significant result improvement against previous methods, this technology may contribute to enhance physical simulations in engineering applications such as computational modelling, digital twins or artificial/virtual reality. © 2024 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.