Spatiotemporal Learning on Cell-embedded Graphs
Keywords: Spatiotemporal Dynamics, Graph Learning, Physics-embeded Learning
TL;DR: Proposed a cell-embedded GNN model (aka, CeGNN) to learn spatiotemporal dynamics with lifted performance.
Abstract: Data-driven simulation of physical systems has recently kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in predicting spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message passing mechanism in GNNs limits the model's representation learning ability. In this paper, we proposed a cell-embedded GNN model (aka, CeGNN) to learn spatiotemporal dynamics with lifted performance. Specifically, we introduce a learnable cell attribution to the 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 to edge and then to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the performance of CeGNN and alleviate the over-smoothness problem, via treating the latent features as basis functions. The extensive experiments on various PDE systems and one real-world dataset demonstrate that CeGNN achieves superior performance compared with other baseline models, significantly reducing the prediction errors on several PDE systems.
Primary Area: learning on time series and dynamical systems
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Submission Number: 4916
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