Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN

Abstract: Learning the physical simulation on large-scale meshes with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. There has been growing interest in the community to introduce \textit{multi-scale} structures to GNNs for physical simulation. However, current state-of-the-art methods are limited by their reliance on the labor-intensive drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, \textit{bi-stride} to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the breadth-first search (BFS), without the need for the manual drawing of coarser meshes and avoiding the wrong edges by spatial proximity. Additionally, it enables a one-MP scheme per level and non-parametrized pooling and unpooling by interpolations, resembling U-Nets, which significantly reduces computational costs. Experiments show that the proposed framework, \textit{BSMS-GNN}, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physical simulations.