Discovering Message Passing Hierarchies for Mesh-Based Physics Simulation

Huayu Deng, Xiangming Zhu, Yunbo Wang, Xiaokang Yang

Keywords: Physics Simulation, Message Passing Networks

Abstract: Graph neural networks have emerged as a powerful tool for large-scale mesh-based physics simulation. Existing approaches primarily employ hierarchical, multi-scale message passing to capture long-range dependencies within the graph. However, these graph hierarchies are typically fixed and manually designed, which do not adapt to the evolving dynamics present in complex physical systems. In this paper, we introduce a novel neural network named DHMP, which learns **D**ynamic **H**ierarchies for **M**essage **P**assing networks through a differentiable node selection method. The key component is the *anisotropic* message passing mechanism, which operates at both intra-level and inter-level interactions. Unlike existing methods, it first supports directionally non-uniform aggregation of dynamic features between adjacent nodes within each graph hierarchy. Second, it determines node selection probabilities for the next hierarchy according to different physical contexts, thereby creating more flexible message shortcuts for learning remote node relations. Our experiments demonstrate the effectiveness of DHMP, achieving $22.7$\% improvement on average compared to recent fixed-hierarchy message passing networks across five classic physics simulation datasets.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 5636