{"ID":2871931,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10659","arxiv_id":"2509.10659","title":"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.","short_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 topolog...","url_abs":"https://arxiv.org/abs/2509.10659","url_pdf":"https://arxiv.org/pdf/2509.10659v1","authors":"[\"Bo Lei\",\"Victor M. Castillo\",\"Yeping Hu\"]","published":"2025-09-12T19:38:38Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\",\"physics.comp-ph\"]","methods":"[\"Graph Neural Network\",\"Transformer\"]","has_code":false}