HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks

Researchers propose HI-MeshGraphNets (HI-MGN), a hierarchical multi-scale graph neural network that improves mesh-based physics simulation accuracy and efficiency. In benchmarks on three structural and fluid problems, HI-MGN outperforms MeshGraphNets and Bi-Stride Multi-Scale GNN while reducing training time and peak memory usage.

arXiv:2608.13827v1 Announce Type: new Abstract: Machine-learned physical surrogate models have become promising alternatives to mesh-based numerical solvers. Among them, graph neural networks GNNs are well suited for representing simulation meshes and learning nodal state evolution through message passing. However, conventional flat message passing becomes inefficient on large, high-fidelity meshes because information propagates only one hop per layer, requiring deep processors for long-range interactions and increasing computational cost, memory usage, and the risk of over-smoothing. To address this limitation, we propose Hierarchical Interpolating MeshGraphNets HI-MGN , a multiscale extension of MeshGraphNets for efficient long-range communication on unstructured meshes. HI-MGN replaces the flat processor with a hierarchical multiscale processor that coarsens graphs using farthest-point sampling and Voronoi partitioning while preserving the original mesh topology. Message passing on coarse graphs enables information to travel over larger geometric distances with fewer layers, and a learned graph interpolation network reconstructs fine-resolution features. Across three structural and fluid benchmarks, HI-MGN achieves improved accuracy compared with MeshGraphNets and the Bi-Stride Multi-Scale GNN while reducing training time and peak memory usage. The results show that topology-aware hierarchical message passing and learned coarse-to-fine interpolation provide an effective and practical framework for scalable mesh-based physics surrogate modeling.