🤖 AI Summary
Existing grid-based graph neural networks (GNNs) are constrained by first-order node-edge message passing, limiting their ability to capture high-order spatial dependencies among regional features and voxel-level geometric information in physical systems. Method: We propose the Cell-embedded Graph Neural Network (CeGNN), which introduces a novel learnable cell-attribute embedding mechanism that extends message passing from “edge→node” to “cell→edge→node”, explicitly encoding local geometric structure; additionally, we design a basis-function-driven feature enhancement module that mitigates over-smoothing by leveraging implicit features as functional bases. Contribution/Results: Evaluated on diverse PDE-solving tasks and real-world physical datasets, CeGNN consistently outperforms state-of-the-art GNN baselines, achieving up to an order-of-magnitude reduction in prediction error. This work establishes a new paradigm for data-driven physics simulation—uniquely balancing expressive power with geometric awareness.
📝 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 the 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 relieve 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, particularly reducing the prediction error with up to 1 orders of magnitude on several PDE systems.