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DragSolver: A Multi-Scale Transformer for Real-World Automotive Drag Coefficient Estimation

ICML 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Machine learning for physical simulation

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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

Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use DragSolver instead of the strongest baseline, Mamba3DAutomotive drag coefficient prediction · DrivAerNetRelative L2: 0.0015 -> 0.0007± 0.0001Helped
Use DragSolver instead of the strongest baseline, Mamba3DAutomotive drag coefficient prediction · DrivAerNet++Relative L2: 0.0014 -> 0.0005± 0.0001Helped
Use DragSolver instead of Mamba3DCross-shape prediction on DrivAerNet++ estateback (train F+N) · DrivAerNet++ estatebackRelative L2: 0.0097 -> 0.0031± 0.0003Helped
Use DragSolver instead of Mamba3DCross-shape prediction on DrivAerNet++ notchback (train F+E) · DrivAerNet++ notchbackRelative L2: 0.0054 -> 0.0034± 0.0003Helped
Use DragSolver instead of Mamba3DCross-dataset prediction · DrivaerML (train DrivAerNet++)Relative L2: 0.0197 -> 0.0091± 0.0001Helped
Add multi-scale feature fusion (ablation)DragSolver · DrivAerNet++ in-distributionRelative L2: 0.0049 -> 0.0026Helped
Add multi-scale feature fusion (ablation)DragSolver · DrivAerNet++ cross-shapeRelative L2: 0.0081 -> 0.0065Helped
Add heterogeneous scale normalization (ablation)DragSolver with multi-scale features · DrivAerNet++ in-distributionRelative L2: 0.0026 -> 0.0007Helped
Add surface-guided gating (ablation)DragSolver with multi-scale features and normalization · DrivAerNet++ interior mismatchRelative L2: 0.0057 -> 0.0024Helped
Set multi-scale depth to L=5 rather than L=1 (ablation)DragSolver · DrivAerNet++Relative L2: 0.0020 -> 0.0008Helped
Use max instead of mean global pooling (ablation)DragSolver · DrivAerNet++Relative L2: 0.0009 -> 0.0007Helped
Increase voxel size from 0.01 to 0.05 or 0.1 (ablation)DragSolver · DrivAerNet++Relative L2: 0.0009 -> 0.0016; 0.0009 -> 0.0029Hurt

Surprising findings

Limitations

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

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