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GeoTransolver: Learning Physics on Irregular Domains using Multi-scale Geometry Aware Physics Attention Transformer
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Proposes GeoTransolver, a Transolver extension with GALE attention that cross-attends at every block to a shared multi-scale ball-query geometry and global-parameter context, evaluated on DrivAerML, SHIFT-SUV/Wing and two crash-dynamics benchmarks.
Problem
Transformer neural operators for CAE lose geometric and operating-regime information with depth and struggle with multi-scale, non-uniform industrial meshes.
Approach
GALE attention pairs Transolver physics attention on learned slices with cross-attention to a geometry/global context built from multi-scale ball queries and projected into the same slice-token space, reused at every layer via a learnable gate.
Key results
- On SHIFT-SUV/Wing volume fields, GeoTransolver achieves the lowest relative L1 error on nearly all columns, e.g. Ma=0.85 u error 2.00% vs 9.51% for AB-UPT and 3.72% for Transolver.
- On DrivAerML, the best 20-layer, 29M-parameter configuration reaches surface pressure L1 error 2.86% and volume velocity error 4.02%, with C_D R^2 0.996.
- On crash benchmarks, GeoTransolver with FLARE backend lowers relative L2 error from 9.12e-3 (Transolver) to 6.80e-3 on bumper beam and from 1.60e-2 to 8.95e-3 on BIW.
Surprising findings
- On SHIFT-Wing, all models reach R^2=1.0 on drag and lift, so integral force metrics do not discriminate.
- DoMINO (trained per-Mach) achieves lower wall-shear error than GeoTransolver at Mach 0.5 on SHIFT-Wing.
Limitations
- Multi-scale ball-query context increases per-step training and inference cost (about 2.1x).
- Out-of-distribution extreme-drag DrivAerML designs remain the hardest cases and are not directly addressed.
- Crash-dynamics evaluation is limited to two datasets over short horizons.
Experimental setup
Datasets: DrivAerML Luminary SHIFT-SUV Luminary SHIFT-Wing bumper-beam crash dataset Body-in-White frontal-impact crash dataset
Benchmarks: DrivAerML SHIFT-SUV SHIFT-Wing bumper-beam crash BIW crash
Metrics: relative L1 error R^2 drag/lift relative L2 error probe kinematic MSE
Baselines: Domino Transolver AB-UPT GAOT FLARE
Builds on: Transolver Domino FLARE GAOT
Closest papers by meaning
- Transolver: A Fast Transformer Solver for PDEs on General Geometries (ICML 2024 · similarity 0.85)
- Attention on the Sphere (NeurIPS 2025 · similarity 0.85)
- Geometry Aware Operator Transformer as an efficient and accurate neural surrogate for PDEs on arbitrary domains (NeurIPS 2025 · similarity 0.85)
- Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators (NeurIPS 2024 · similarity 0.85)
- AeroGTO: An Efficient Graph-Transformer Operator for Learning Large-Scale Aerodynamics of 3D Vehicle Geometries (AAAI 2025 · similarity 0.84)
- SEA: State-Exchange Attention for High-Fidelity Physics Based Transformers (NeurIPS 2024 · similarity 0.84)
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