Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics

• URL: http://arxiv.org/abs/2304.00338v1
• Date: Sat, 1 Apr 2023 15:42:18 GMT
• Title: Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics
• Authors: Brian R. Bartoldson, Yeping Hu, Amar Saini, Jose Cadena, Yucheng Fu, Jie Bao, Zhijie Xu, Brenda Ng, Phan Nguyen
• Abstract summary: MeshGraphNets (MGN) is a subclass of GNNs for mesh-based physics modeling. We train MGN on meshes with textitmillions of nodes to generate computational fluid dynamics simulations. This work presents a practical path to scaling MGN for real-world applications.
• Score: 6.360914973656273
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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