Physically Aligned Hierarchical Mesh-based Network for Dynamic System Simulation

Bo Lei, Victor M Castillo, Yeping Hu

Keywords: dynamic system; physics simulation; solid mechanics; graph-based simulation;

Abstract: Dynamic systems evolve through complex interactions, where local events influence global behaviors, reflecting the interconnected nature of real-world phenomena. Simulating such systems demands models that effectively capture both local and long-range dynamics, while maintaining a balance between accuracy and computational efficiency. However, existing mesh-based Graph Neural Network (GNN) methods often struggle to achieve both high accuracy and efficiency, especially when dealing with large datasets, complex mesh structures, and extensive long-range effects. Inspired by how real-world dynamic systems operate, we present the Mesh-based Multi-Segment Graph Network (MMSGN), a novel framework designed to address these challenges by leveraging a physically aligned hierarchical information exchange mechanism. MMSGN combines micro-level local interactions with macro-level global exchanges, aligning the hierarchical mesh structure with the system’s physical properties to seamlessly capture both local and global dynamics. This approach enables precise modeling of complex behaviors while maintaining computational efficiency. We validate our model on multiple dynamic system datasets and compare it with several state-of-the-art methods. Our results demonstrate that MMSGN delivers superior accuracy and mesh quality, excels in managing long-range effects, and maintains high computational efficiency. Furthermore, MMSGN exhibits strong generalization capabilities, scaling effectively to larger physical domains. These advantages make MMSGN well-suited for simulating complex, large-scale dynamic systems across a variety of scenarios. Codes and data will be made publicly accessible upon acceptance.

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

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Submission Number: 3197