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Geometry Aware Operator Transformer as an efficient and accurate neural surrogate for PDEs on arbitrary domains
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Proposes GAOT, a geometry-aware operator transformer with multiscale attentional graph neural operator encoder/decoder, geometry statistical embeddings, and a ViT processor for PDE learning on arbitrary domains, claiming accuracy, efficiency and SOTA on large 3D industrial CFD datasets.
Problem
Learning PDE solution operators on arbitrary (complex, varying) domains accurately and efficiently; existing models trade accuracy against computational efficiency and scalability.
Approach
Encode arbitrary point clouds to a latent regular grid via multiscale attentional graph neural operators (attention-based quadrature) fused with local statistical geometry embeddings, process with a patch-based vision transformer, and decode to any query point with a mirrored MAGNO decoder.
Key results
- On time-independent datasets GAOT is best on 5 of 7 (e.g., Poisson-C-Sines 3.10% vs RIGNO-18 6.83%) and reports ~50% lower average error than RIGNO-18, per the paper.
- GAOT achieves 97.5 samples/s training throughput and 6.97 ms latency on an RTX 4090, ~50% higher throughput and ~15% lower latency than GINO.
- On DrivAerNet++, GAOT reaches pressure MSE 4.27e-2 and wall shear stress MAE 1.54e-1, beating FIGConvNet, TripNet and RegDGCNN leaderboard baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GAOT instead of RIGNO-18 | PDE operator learning · Time-independent datasets | relative L1 error: almost 50% more accurate | Helped |
| Use GAOT instead of RIGNO-18 | PDE operator learning · Time-dependent datasets | relative L1 error | Helped |
| Use GAOT instead of baseline models | PDE surrogate inference · Variable-geometry learning tasks | training throughput: almost 50% | Helped |
| Use GAOT instead of baseline models | PDE surrogate inference · Variable-geometry learning tasks | inference latency: 15% | Helped |
| Add MAGNO encoder/decoder instead of message-passing encoders/decoders (ablation) | GAOT · PDE benchmarks | accuracy | Helped |
| Use a regular equispaced latent point cloud instead of downsampled points or a projected low-dimensional grid (ablation) | GAOT · PDE benchmarks | accuracy | Helped |
| Vary the latent grid size (ablation) | GAOT · PDE benchmarks | robustness | No clear effect |
| Use time-derivative marching (γ=1, δ=τ) instead of other time-stepping choices (ablation) | GAOT · Time-dependent PDEs | accuracy | Helped |
| Use statistical geometry embeddings instead of no geometry features or PointNet geometry features (ablation) | GAOT · PDE benchmarks | accuracy | Helped |
| Add multiscale features instead of a single-scale GNO encoder/decoder (ablation) | GAOT · PDE benchmarks | accuracy | Helped |
| Use MAGNO encoder/decoder alongside the ViT processor rather than relying on the ViT processor alone (ablation) | GAOT · PDE benchmarks | accuracy | Helped |
| Fine-tune a pretrained GAOT instead of training from scratch | GAOT · Unseen bluff-body shapes | accuracy: almost an order of magnitude gain | Helped |
Surprising findings
- Transolver and GNOT scale so poorly in training throughput that they could not be trained on the large-scale time-dependent datasets with all2all training.
Limitations
- Efficiency and scalability comparisons limited to a few baselines (RIGNO-18, GINO, Transolver) and one GPU.
- Large 3D industrial results only compared against GINO on DrivAerML and NASA CRM, since other models could not be run at that scale.
Experimental setup
Datasets: Poisson-Gauss Poisson-C-Sines Elasticity NACA0012 NACA2412 RAE2822 Bluff-Body NS-Gauss NS-PwC NS-SL NS-SVS CE-Gauss
Benchmarks: Poisson-Gauss Poisson-C-Sines Elasticity NACA0012 NACA2412 RAE2822 Bluff-Body NS-Gauss NS-PwC NS-SL NS-SVS CE-Gauss
Metrics: median relative L1 error MSE mean absolute error training throughput inference latency robustness score
Baselines: RIGNO-18 Transolver GNOT UPT GINO GeoFNO FNO DSE FIGConvNet TripNet RegDGCNN
Builds on: GINO FNO AGNO ViT all2all training
Closest papers by meaning
- CViT: Continuous Vision Transformer for Operator Learning (ICLR 2025 · similarity 0.89)
- RIGNO: A Graph-based Framework For Robust And Accurate Operator Learning For PDEs On Arbitrary Domains (NeurIPS 2025 · similarity 0.89)
- GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems (NeurIPS 2026 · similarity 0.88)
- Adaptive Coordinate Transforms for Neural Operators (NeurIPS 2026 · similarity 0.88)
- PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations (ICML 2025 · similarity 0.87)
- AeroGTO: An Efficient Graph-Transformer Operator for Learning Large-Scale Aerodynamics of 3D Vehicle Geometries (AAAI 2025 · similarity 0.87)
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