Graph neural networks informed locally by thermodynamics
This work addresses a computational bottleneck for researchers in solid and fluid mechanics by enabling more efficient and scalable thermodynamics-informed graph neural networks, though it is incremental as it builds on existing metriplectic frameworks.
The authors tackled the problem of preserving local structure in thermodynamics-informed graph neural networks by developing a local version of metriplectic biases, which avoids assembling global matrices. This approach demonstrated significant computational efficiency and strong generalization, accurately inferring examples different from training data.
Thermodynamics-informed neural networks employ inductive biases for the enforcement of the first and second principles of thermodynamics. To construct these biases, a metriplectic evolution of the system is assumed. This provides excellent results, when compared to uninformed, black box networks. While the degree of accuracy can be increased in one or two orders of magnitude, in the case of graph networks, this requires assembling global Poisson and dissipation matrices, which breaks the local structure of such networks. In order to avoid this drawback, a local version of the metriplectic biases has been developed in this work, which avoids the aforementioned matrix assembly, thus preserving the node-by-node structure of the graph networks. We apply this framework for examples in the fields of solid and fluid mechanics. Our approach demonstrates significant computational efficiency and strong generalization capabilities, accurately making inferences on examples significantly different from those encountered during training.