Thermodynamics-informed graph neural networks
This work addresses modeling non-conservative dynamics in physics and engineering, offering a domain-specific improvement over existing methods.
The paper tackled predicting the evolution of dissipative dynamic systems by incorporating geometric and thermodynamic biases into graph neural networks, achieving relative mean errors under 3% in fluid and solid mechanics examples.
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.