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：数据驱动建模方法可以产生用于研究大尺度物理问题的快速替代模型。其中，在基于网格的数据上操作的图神经网络（GNN）很受欢迎，因为它们具有促进物理忠实度的归纳偏差，但硬件限制限制了它们在大型计算域中的应用。我们展示了一类可以在3D网格上训练的GNN替代模型。通过我们的域分解方法，我们将MeshGraphNets（MGN）这一基于网格的物理建模方法进行了扩展，以促进数学上相当于在特定条件下在整个域上训练的训练。通过这种方法，我们能够训练MGN模型在拥有数百万节点的网格上生成计算流体动力学（CFD）模拟结果。此外，我们展示了如何通过高阶数值积分增强MGN模型，以降低模型的误差和训练时间。我们在一个包含3.1M节点的网格上生成的3D $\text{CO}_2$ 捕捉CFD模拟数据集上验证了我们的方法。该研究提供了一个实用的扩展MGN模型以应用于实际世界问题的途径。