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EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions
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Proposes DHMP (EvoMesh), a fully differentiable GNN that learns time-evolving, physics-conditioned mesh hierarchies via Gumbel-Softmax node selection and anisotropic message passing for mesh-based physical simulation.
Problem
Hierarchical GNN simulators for mesh-based physics use manually designed, fixed graph hierarchies that cannot adapt to evolving dynamics or varying physical contexts.
Approach
Jointly learns graph hierarchies and dynamics: an anisotropic message passing layer computes learnable edge importance weights that are reused for inter-level REDUCE/EXPAND, while a node update head outputs retain/discard probabilities sampled with straight-through Gumbel-Softmax to build the next coarser level at each step, with K-hop edge enhancement (K=2).
Key results
- On the standard benchmarks, DHMP reports RMSE-All of 6.571e-2 on CylinderFlow versus 16.98e-2 for the second-best BSMS-GNN, a 61.3% promotion.
- On out-of-distribution mesh resolutions, DHMP achieves RMSE-1 of 0.4855e-2 on CylinderFlow versus 0.9177e-2 for BSMS-GNN, and does not win on FlyingFlag and DeformingPlate where MGN is better.
- On paper folding with time-varying meshes, DHMP reduces RMSE-All from 24.08e-2 (MGN) to 7.412e-2 (69.2% promotion).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DHMP instead of the strongest fixed-hierarchy baseline | mesh-based physical simulation · CylinderFlow, Airfoil, Flag, DeformingPlate | RMSE-All (×10⁻²): 6.571 vs 16.98; 2002 vs 2080; 76.16 vs 90.32; 1.296 vs 1.811 | Helped |
| use DHMP instead of MGN | mesh-based physical simulation with time-varying meshes · FoldingPaper | RMSE-All (×10⁻²): 24.08 -> 7.412 | Helped |
| add anisotropic intra-level propagation (ablation) | DHMP with static Bi-stride hierarchy and unlearnable inter-level propagation · CylinderFlow, Flag | RMSE-All (×10⁻²): 16.98 -> 9.621; 168.1 -> 121.1 | Helped |
| add learnable inter-level propagation (ablation) | static Bi-stride hierarchy with anisotropic propagation · CylinderFlow, Flag | RMSE-All (×10⁻²): 9.621 -> 8.317; 121.1 -> 109.9 | Helped |
| add learnable inter-level propagation (ablation) | dynamic hierarchy with anisotropic propagation · CylinderFlow, Flag | RMSE-All (×10⁻²): 7.793 -> 6.571; 82.65 -> 76.16 | Helped |
| replace uniform node sampling with adaptive, data-aware hierarchy construction (ablation) | anisotropic propagation with learnable inter-level updates · CylinderFlow, Flag | RMSE-All (×10⁻²): 9.357 -> 6.571; 145.27 -> 76.16 | Helped |
| replace MLP-based AMP with GATConv (ablation) | DHMP · CylinderFlow, Flag | RMSE-All (×10⁻²): 6.571 -> 10.253; 76.16 -> 106.2 | Hurt |
| replace MLP-based AMP with cross-attention (ablation) | DHMP · CylinderFlow, Flag | RMSE-All (×10⁻²): 6.571 -> 8.356; 76.16 -> 75.12 | Mixed |
| use K=1 instead of K=2 for edge enhancement (ablation) | DHMP · Flag | RMSE-All (×10⁻²): 76.16 -> 100.1 | Hurt |
| vary edge enhancement from K=2 to K=3 (ablation) | DHMP · Flag | RMSE-All (×10⁻²): 76.16 -> 86.84 | Hurt |
| vary edge enhancement from K=2 to K=4 (ablation) | DHMP · Flag | RMSE-All (×10⁻²): 76.16 -> 105.4 | Hurt |
Surprising findings
- MGN achieves lower errors than DHMP on the FlyingFlag and DeformingPlate OOD resolution tests, showing fixed mesh architectures remain competitive on regular structures.
- Replacing the MLP-based AMP weight network with cross-attention or GATConv yields worse results than the default MLP design on Cylinder and Flag.
Limitations
- Learned hierarchies are not yet interpretable.
- Does not achieve full resolution-free generalization across arbitrary mesh resolutions.
- Underperforms MGN on FlyingFlag and DeformingPlate in OOD resolution tests.
Experimental setup
Datasets: CylinderFlow Airfoil Flag DeformingPlate FoldingPaper
Benchmarks: CylinderFlow Airfoil Flag DeformingPlate FoldingPaper
Metrics: RMSE-1 RMSE-All RMSE-50
Baselines: MGN Lino et al. BSMS-GNN Eagle HCMT GATConv variant
Builds on: MeshGraphNets BSMS-GNN Gumbel-Softmax Graph Attention Networks
Closest papers by meaning
- MaNGO — Adaptable Graph Network Simulators via Meta-Learning (NeurIPS 2025 · similarity 0.86)
- Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics (NeurIPS 2025 · similarity 0.85)
- AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction (NeurIPS 2025 · similarity 0.85)
- UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss (NeurIPS 2025 · similarity 0.85)
- Point Cloud Sequence Encoding for Material-conditioned Graph Network Simulators (NeurIPS 2026 · similarity 0.85)
- Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks (ICLR 2025 · similarity 0.85)
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