通过体素信息传递提升物理系统动态建模能力
Spatiotemporal Graph Learning with Direct Volumetric Information Passing and Feature Enhancement
- 引入单元嵌入机制，实现从体积到节点的高阶信息传递
- 在多个偏微分方程系统上优于现有基线模型
- 适合需要精确时空建模的科学计算与仿真任务
基于数据的物理系统学习受到广泛关注，众多神经网络模型被提出。特别是基于网格的图神经网络（GNN）在任意几何域上的时空动力学建模中展现出巨大潜力。然而，现有GNN中的节点-边消息传递与聚合机制限制了表征学习能力。本文提出双模块框架——单元嵌入与特征增强图神经网络（CeFeGNN），用于学习时空动态。具体地，将可学习的单元属性嵌入到常见的节点-边消息传递过程中，更好地捕捉区域特征的空间依赖性。该策略本质上将局部聚合方案从一阶（如边到节点）升级为高阶（如体素和边到节点），利用消息传递中的体素信息。同时，设计新型特征增强模块以进一步提升性能并缓解过平滑问题。在多种偏微分方程系统及一个真实世界数据集上的大量实验表明，CeFeGNN相比其他基线模型表现更优。
原文摘要 · Abstract (English)
Data-driven learning of physical systems has kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in modeling spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message-passing and aggregation mechanism in GNNs limits the representation learning ability. In this paper, we proposed a dual-module framework, Cell-embedded and Feature-enhanced Graph Neural Network (aka, CeFeGNN), for learning spatiotemporal dynamics. Specifically, we embed learnable cell attributions to the common node-edge message passing process, which better captures the spatial dependency of regional features. Such a strategy essentially upgrades the local aggregation scheme from first order (e.g., from edge to node) to a higher order (e.g., from volume and edge to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the model's performance and alleviate the over-smoothness problem. Extensive experiments on various PDE systems and one real-world dataset demonstrate that CeFeGNN achieves superior performance compared with other baselines.
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