Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is possible to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with millions of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. This work presents a practical path to scaling MGN for real-world applications. Understanding physical systems and engineering processes often requires extensive numerical simulations of their underlying models. However, these simulations are typically computationally expensive to generate, which can hinder their applicability to large-scale problems.