2023/04/01 by Brian R. Bartoldson, Bartoldson, Brian R., Yeping Hu +15
Computer Science · #Computational Physics and Python Applications #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and Data Classification #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2304.00338
openalex publication_date 2023/04/01 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28
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. We validated our methods on an accompanying dataset of 3D CO2-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications.