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.

翻译：数据驱动建模方法能够生成快速替代模型，用于研究大规模物理问题。其中，基于网格数据操作的图神经网络（GNNs）因其具备促进物理忠实性的归纳偏置而受到青睐，但硬件限制阻碍了其在大型计算域中的应用。我们证明，在三维网格上训练一类GNN替代模型是\textit{可行的}。通过我们的域分解方法，我们扩展了MeshGraphNets（MGN）——一类用于基于网格物理建模的GNN子类——使得在特定条件下，其训练在数学上等价于在全域上训练。借助该方法，我们成功在包含\textit{数百万}节点的网格上训练了MGN，以生成计算流体动力学（CFD）模拟。此外，我们展示了如何通过高阶数值积分增强MGN，从而降低其误差并缩短训练时间。我们基于一个包含310万节点网格的三维$\text{CO}_2$捕集CFD模拟数据集验证了所提方法。本研究为将MGN扩展至实际应用提供了一条可行路径。