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

• URL: http://arxiv.org/abs/2509.10659v1
• Date: Fri, 12 Sep 2025 19:38:38 GMT
• Title: M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations
• Abstract summary: Mesh-based graph neural networks (GNNs) have become effective surrogates for PDE simulations.<n>We develop M4GN, a three-tier, segment-centric hierarchical network.<n>We show that M4GN improves prediction accuracy by up to 56% while achieving up to 22% faster inference than state-of-the-art baselines.
• Score: 11.547387701986784
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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