M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912585408839680 |
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| author | Lei, Bo Castillo, Victor M. Hu, Yeping |
| author_facet | Lei, Bo Castillo, Victor M. Hu, Yeping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations Lei, Bo Castillo, Victor M. Hu, Yeping Machine Learning Computational Engineering, Finance, and Science Computational Physics 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. |
| title | M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations |
| topic | Machine Learning Computational Engineering, Finance, and Science Computational Physics |
| url | https://arxiv.org/abs/2509.10659 |