发表机构
Samsung Electronics Co.; Sejong University（三星电子; 世宗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出HI-MGN，即MeshGraphNets的多尺度扩展，通过分层多尺度处理器与图插值网络，提升非结构化网格物理学习的精度并降低训练时间与内存使用，在三个基准测试中表现优于现有模型。
AI 中文摘要
机器学习得到的物理替代模型已成为基于网格的数值求解器的有前景替代方案，其中图神经网络（GNN）适用于表示模拟网格并通过消息传递学习节点状态演化。然而，传统的平面消息传递在大型高保真网格上效率低下，因为每一层仅传播一跳信息，对于长程交互需要深层处理器，这会增加计算成本、内存使用并加剧过平滑风险。为解决此限制，我们提出Hierarchical Interpolating MeshGraphNets（HI-MGN），即MeshGraphNets的多尺度扩展，用于在非结构化网格上实现高效长程通信。HI-MGN用分层多尺度处理器替代平面处理器，该处理器通过最远点采样和Voronoi划分对图进行粗化，同时保留原始网格拓扑；粗图上的消息传递使信息能以更少层跨越更大几何距离，学习到的图插值网络可重构高分辨率特征。在三个结构和流体基准测试中，HI-MGN相比MeshGraphNets和Bi-Stride多尺度GNN实现了更高精度，同时减少了训练时间和峰值内存使用。结果表明，感知拓扑的分层消息传递与学习到的粗到细插值为可扩展的基于网格的物理替代建模提供了有效实用框架。
英文摘要
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.
