M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations

TMLR Paper4952 Authors

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 Mesh‑based Multi‑segment Hierarchical Graph Network. It starts 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 form an intermediate representation connecting a micro‑level GNN that captures local physics to a macro‑level transformer that exchanges information across segments, achieving a balanced trade‑off between accuracy and computational cost. Evaluated on three representative benchmark datasets, M4GN improves prediction accuracy by up to 56\% while achieving up to 22\% faster inference than state‑of‑the‑art baselines. Code and datasets will be released upon acceptance.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: Gilles Louppe

Submission Number: 4952