M4GN: Mesh-Based Multi-Segment Hierarchical Graph Network for Dynamic Simulations

Abstract

Mesh-based graph neural networks (GNNs) have become effective surrogates for PDE simulations, yet their deep message passing incurs high cost and over‑smoothing on large, long‑range meshes; hierarchical GNNs shorten propagation paths but still face two key obstacles: (i) building coarse graphs that respect mesh topology, geometry, and physical discontinuities, and (ii) maintaining fine-scale accuracy without sacrificing the speed gained from coarsening. We tackle these challenges with M4GN—a three‑tier, segment‑centric hierarchical network. M4GN begins with a hybrid segmentation strategy that pairs a fast graph partitioner with a superpixel‑style refinement guided by modal‑decomposition features, producing contiguous segments of dynamically consistent nodes. These segments are encoded by a permutation‑invariant aggregator, avoiding the order sensitivity and quadratic cost of aggregation approaches used in prior works. The resulting information bridges a micro‑level GNN—which captures local dynamics—and a macro‑level transformer that reasons efficiently across segments, achieving a principled balance between accuracy and efficiency. Evaluated on multiple representative benchmark datasets, M4GN improves prediction accuracy by up to 56\% while achieving up to 22\% faster inference than state‑of‑the‑art baselines.