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DragSolver: A Multi-Scale Transformer for Real-World Automotive Drag Coefficient Estimation
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Proposes DragSolver, a multi-scale Transformer with heterogeneous scale normalization, surface-guided gating, and MC dropout uncertainty to predict automotive drag coefficient from 3D meshes/point clouds.
Problem
Rapid and accurate drag coefficient (Cd) estimation from large-scale, heterogeneous real-world 3D vehicle geometries, which CFD and wind tunnel tests are too slow to support in iterative design.
Approach
Combines multi-stage Transformer encoder with multi-scale global pooling, wheelbase-based and hybrid-sampling normalization, multi-stage gating to suppress interior geometry, and Monte Carlo dropout for epistemic uncertainty in a geometry-to-Cd regression.
Key results
- In-distribution on DrivAerNet++, DragSolver reaches relative L2 0.0005 and R2 0.9712, a 64.2% error promotion over the second-best baseline.
- Cross-dataset (DrivAerNet++ to DrivAerML) relative L2 0.0091 with R2 0.2732, while Mamba3D gets R2 -0.0684.
- Under interior mismatch, gating reduces relative L2 from 0.0057 to 0.0024 (ablation); inference ~0.93 s per sample, ~4.8 s with MC dropout.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DragSolver instead of the strongest baseline, Mamba3D | Automotive drag coefficient prediction · DrivAerNet | Relative L2: 0.0015 -> 0.0007± 0.0001 | Helped |
| Use DragSolver instead of the strongest baseline, Mamba3D | Automotive drag coefficient prediction · DrivAerNet++ | Relative L2: 0.0014 -> 0.0005± 0.0001 | Helped |
| Use DragSolver instead of Mamba3D | Cross-shape prediction on DrivAerNet++ estateback (train F+N) · DrivAerNet++ estateback | Relative L2: 0.0097 -> 0.0031± 0.0003 | Helped |
| Use DragSolver instead of Mamba3D | Cross-shape prediction on DrivAerNet++ notchback (train F+E) · DrivAerNet++ notchback | Relative L2: 0.0054 -> 0.0034± 0.0003 | Helped |
| Use DragSolver instead of Mamba3D | Cross-dataset prediction · DrivaerML (train DrivAerNet++) | Relative L2: 0.0197 -> 0.0091± 0.0001 | Helped |
| Add multi-scale feature fusion (ablation) | DragSolver · DrivAerNet++ in-distribution | Relative L2: 0.0049 -> 0.0026 | Helped |
| Add multi-scale feature fusion (ablation) | DragSolver · DrivAerNet++ cross-shape | Relative L2: 0.0081 -> 0.0065 | Helped |
| Add heterogeneous scale normalization (ablation) | DragSolver with multi-scale features · DrivAerNet++ in-distribution | Relative L2: 0.0026 -> 0.0007 | Helped |
| Add surface-guided gating (ablation) | DragSolver with multi-scale features and normalization · DrivAerNet++ interior mismatch | Relative L2: 0.0057 -> 0.0024 | Helped |
| Set multi-scale depth to L=5 rather than L=1 (ablation) | DragSolver · DrivAerNet++ | Relative L2: 0.0020 -> 0.0008 | Helped |
| Use max instead of mean global pooling (ablation) | DragSolver · DrivAerNet++ | Relative L2: 0.0009 -> 0.0007 | Helped |
| Increase voxel size from 0.01 to 0.05 or 0.1 (ablation) | DragSolver · DrivAerNet++ | Relative L2: 0.0009 -> 0.0016; 0.0009 -> 0.0029 | Hurt |
Surprising findings
- Several neural operator baselines (Transolver, GINO, MeshGraphNet) give negative R2 on the automotive datasets.
- Cross-dataset R2 for DragSolver is only 0.2732, indicating limited transfer despite low relative L2.
Limitations
- Cross-dataset R2 remains low (0.2732), so generalization to different datasets is limited.
- Uncertainty calibration is not evaluated beyond reporting standard deviations; future work mentions expanded calibration.
- Code is promised only upon acceptance; no release link is given in the text.
Experimental setup
Datasets: DrivAerNet++ DrivAerNet DrivAerML
Benchmarks: DrivAerNet DrivAerNet++ DrivAerML
Metrics: relative L2 error R2 score
Baselines: PointNet PointNet++ PointTransformer PointGPT Mamba3D PointTransformer V3 MeshGraphNet RegDGCNN GINO Transolver GNOT
Builds on: Point Transformer V3 Monte Carlo dropout Transolver Point-BERT
Closest papers by meaning
- AeroGTO: An Efficient Graph-Transformer Operator for Learning Large-Scale Aerodynamics of 3D Vehicle Geometries (AAAI 2025 · similarity 0.89)
- DrivAerStar: An Industrial-Grade CFD Dataset for Vehicle Aerodynamic Optimization (NeurIPS 2025 · similarity 0.88)
- DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks (NeurIPS 2024 · similarity 0.87)
- AutoHood3D: A Multi‑Modal Benchmark for Automotive Hood Design and Fluid–Structure Interaction (NeurIPS 2025 · similarity 0.85)
- WindsorML: High-Fidelity Computational Fluid Dynamics Dataset For Automotive Aerodynamics (NeurIPS 2024 · similarity 0.84)
- Aerodynamic Coefficients Prediction via Cross-Attention Fusion and Physical-Informed Training (AAAI 2025 · similarity 0.83)
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