Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics
This work provides a practical solution for scaling mesh-based GNN surrogates in computational fluid dynamics and similar domains, though it is incremental as it builds on existing MeshGraphNets methods.
The authors tackled the problem of scaling graph neural networks (GNNs) for mesh-based physics modeling, which was limited by hardware constraints, by developing a domain decomposition approach that enabled training on meshes with millions of nodes, such as a 3.1M-node mesh for CFD simulations, and enhanced performance with higher-order integration to reduce error and training time.
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 \textit{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 \textit{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. We validated our methods on an accompanying dataset of 3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications.