arXiv:2608.13827cs.LG2026-08

用分层图网络提升网格物理模型效率,长距离信息传播更快更准。

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

论文配图:HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networks
图 1 · 摘自论文原文
  • 构建分层多尺度图网络,通过粗化网格实现远距离信息传递
  • 在三个结构与流体基准上精度更高,训练时间与内存使用降低
  • 适合大规模网格物理模拟,尤其擅长处理高保真复杂场景

基于机器学习的物理代理模型已成为网格数值求解器的有力替代方案。其中,图神经网络(GNN)适合表示模拟网格,并通过消息传递学习节点状态演化。然而,传统平面消息传递在大尺寸高保真网格上效率低下,因信息每层仅传播一跳,需深层网络实现长程交互,导致计算成本、内存占用上升且易过平滑。为此,本文提出分层插值网格图网络(HI-MGN),作为MeshGraphNets的多尺度扩展,实现非结构化网格上的高效长程通信。HI-MGN用最远点采样与沃罗诺伊分割对图进行粗化,保留原始网格拓扑;在粗图上进行消息传递,使信息跨越更大几何距离,减少层数;再通过学习的图插值网络重建细粒度特征。在三个结构与流体基准测试中,相比MeshGraphNets与双步多尺度GNN,HI-MGN精度更高,训练时间与峰值内存使用均降低。结果表明,拓扑感知的分层消息传递与学习的粗到细插值,为可扩展的网格物理代理建模提供了有效实用框架。

原文摘要 · Abstract (English)

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.

图神经网络物理模拟多尺度建模网格处理

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