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MeshMask: Physics-Based Simulations with Masked Graph Neural Networks
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Proposes masked pre-training for mesh GNNs in CFD: randomly removing up to 40% of mesh nodes, an asymmetric encoder-decoder, and gated MLP processors, evaluated on seven CFD datasets including a new 3D intracranial aneurysm dataset.
Problem
Training GNN surrogates for CFD on large unstructured meshes is slow and data-hungry, and long-horizon autoregressive rollout error remains high.
Approach
Mask a large fraction of mesh nodes (and their edges) during pre-training so the encoder sees a much smaller graph, reconstruct the full mesh with a shared [MASKED] token and a lightweight decoder, then finetune only the encoder on next-step prediction; combined with gated MLP processors and multigrid W-cycle blocks.
Key results
- On Cylinder, all-rollout RMSE drops from 56.9e-3 (best prior Multigrid/BSMS-GNN) to 29e-3, roughly 49% lower.
- Across seven datasets, the method reports best all-rollout RMSE on all listed datasets, e.g. 3D-Aneurysm 8772e-3 vs 10993e-3 for BSMS-GNN.
- Pretraining on Cylinder and Bezier jointly reduces all-rollout RMSE by 22.7% on Cylinder and 15.6% on Bezier while training 33% faster.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| pre-train on next-step prediction rather than reconstruction (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 86 -> 52 | Helped |
| use Gated MLP rather than MLP at depth 15 (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 72 -> 58 | Helped |
| use Gated MLP rather than MLP at depth 5 (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 185 -> 71 | Helped |
| remove the [MASKED] token from the encoder (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 54.3 -> 52 | Helped |
| remove the [MASKED] token from the encoder (ablation) | MeshMask on Cylinder · Cylinder | FLOPS: 2.8× -> 1× | Helped |
| increase decoder message-passing depth from 1 to 3 (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 49 -> 46 | Helped |
| increase decoder message-passing depth from 3 to 5 (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 46 -> 45 | Helped |
| increase masking ratio into the 25%–40% range (ablation) | MeshMask fine-tuning · CylinderFlow | all-rollout RMSE | Helped |
| add K-hop edges for masking ratios above 20% (K=2 or K=3) (ablation) | MeshMask pre-training · Cylinder | prediction performance | Helped |
| pre-train the same MeshGraphNet for 500k steps with 40% masking (ablation) | MeshGraphNet · CFD datasets | performance: +25% | Helped |
| use GAT rather than Gated MLP processing layers at depth 15 (ablation) | MeshMask on Cylinder · Cylinder | all-rollout RMSE (×10^-3): 58 -> 58.2 | No clear effect |
| pre-train on Cylinder before fine-tuning on Bezier (ablation) | MeshMask · Bezier | all-rollout RMSE (×10^-3): 275 -> 315 | Hurt |
Surprising findings
- One-step RMSE shows minimal or no improvement from masking, while long-horizon rollout error improves substantially.
- Removing the [MASKED] token in the encoder gives slightly better all-rollout RMSE (52 vs 54.3) at 1x rather than 2.8x FLOPS.
Limitations
- Gains in one-step RMSE are minimal, so benefit is mostly in long-horizon rollouts.
- Gated MLP variant increases parameters substantially (9.2M vs 2.8M) and vRAM (16 GB vs 7 GB).
- Code is promised only after publication; no release stated in the text.
Experimental setup
Datasets: Cylinder Plate FlagSimple Airfoil Bezier 2D-Aneurysm 3D-Aneurysm
Benchmarks: Cylinder Plate FlagSimple Airfoil Bezier 2D-Aneurysm 3D-Aneurysm
Metrics: one-step RMSE all-rollout RMSE inference time vRAM parameters
Baselines: MeshGraphNet (MGN) Multigrid MultiScaleGNN BSMS-GNN MGN w/ masking
Builds on: MeshGraphNet masked autoencoders Multigrid GNN (MultiScaleGNN) BSMS-GNN
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