In this study, we introduce a domain-decomposition-based distributed training
and inference approach for message-passing neural networks (MPNN). Our
objective is to address the challenge of scaling edge-based graph neural
networks as the number of nodes increases. Through our distributed training
approach, coupled with Nystr\"om-approximation sampling techniques, we present
a scalable graph neural network, referred to as DS-MPNN (D and S standing for
distributed and sampled, respectively), capable of scaling up to $O(10^5)$
nodes. We validate our sampling and distributed training approach on two cases:
(a) a Darcy flow dataset and (b) steady RANS simulations of 2-D airfoils,
providing comparisons with both single-GPU implementation and node-based graph
convolution networks (GCNs). The DS-MPNN model demonstrates comparable accuracy
to single-GPU implementation, can accommodate a significantly larger number of
nodes compared to the single-GPU variant (S-MPNN), and significantly
outperforms the node-based GCN.

本研究介绍了一种基于领域分解的分布式训练和推理方法，用于消息传递神经网络 (MPNN)。我们的目标是解决随着节点数量增加，无线边缘网络的规模化问题。通过我们的分布式训练方法，并结合 NystrÖm 近似采样技术，我们提出了一种可扩展的图神经网络，称为 DS-MPNN (D 和 S 分别代表分布式和采样)，能够扩展到 O (10^5) 个节点。我们在两个案例上验证了我们的采样和分布式训练方法：(a) Darcy 流数据集和 (b) 二维翼型稳态 RANS 模拟，与单 GPU 实现和基于节点的图卷积网络 (GCN) 进行比较。DS-MPNN 模型展示了与单 GPU 实现相当的准确性，可以容纳比单 GPU 变体 (S-MPNN) 更多的节点，并且明显优于基于节点的 GCN。