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.

本文讲解了如何通过域分解方案将 MeshGraphNets（MGN）应用于具有百万节点的 3D 网格，进而生成计算流体力学（CFD）模拟结果，并通过高阶数值积分技术提高 MGN 的准确性和训练时间，为其在实际应用中的大规模使用提供了有效的路径。