MPG: An Efficient Multi-scale Point-Based GNN for Non-uniform Meshes

Qinxin Wu, Pengwei Liu, Xingyu Ren, Dong Ni

Abstract: Graph Neural Networks (GNNs) have become a powerful tool for modeling complex physical simulations, leveraging their ability to learn from irregular data representations. However, non-uniform meshes introduce significant challenges, particularly in adaptive multi-scale sampling, topological reconstruction, and efficient feature aggregation, often leading to high computational costs. Existing methods struggle to balance efficiency and accuracy due to their inability to dynamically adapt to irregular mesh structures. To address these limitations, we introduce Multi-Scale Point-Based Graph Neural Networks (MPG), a framework that combines point-cloud downsampling with topology-constrained strategies. MPG employs density-aware hierarchical sampling to adaptively retain critical nodes while leveraging a learnable neighborhood aggregation mechanism to enhance local structural sensitivity. Additionally, we introduce adaptive Constrained Delaunay reconstruction, which preserves global topology by eliminating invalid edges and maintaining boundary constraints during coarsening. To further improve efficiency, our model integrates lightweight residual MLPs, enabling scalable dimensions on multi-scale features. MPG’s architecture supports dynamic multi-scale compression across diverse physical domains. Evaluations on fluid dynamics, thermochemical reactions, and cavity flow demonstrate that MPG reduces parameter count by at least \(84.5\%\) and accelerates training by \(17.7\%\sim 86.1\%\) per epoch compared to baseline models, while maintaining high single-step rollout accuracy (RMSE\(<10^{-2}\)). These results establish MPG as a new benchmark for efficient and accurate simulations on non-uniform meshes, offering a versatile solution for complex physical systems.