Spatiotemporal Graph Learning with Direct Volumetric Information Passing and Feature Enhancement

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.