PaperlayerView exact revision on arXiv

Source-linked AI summary

HGPTrans: Hierarchical Graph-Pooling Transolver for Automotive Aerodynamic Drag Coefficient Prediction

Bo Liu, Fengli Zhang, Qiuli Luo, Lianrui Nie, Wenjiang Wang

arXiv:2609.31765v2cs.CVphysics.flu-dyn

TL;DR

High-fidelity CFD provides reliable drag estimates but can take hours to days per vehicle, limiting large-scale design screening. HGPTrans predicts drag from vehicle meshes using local graph features, global slice attention, and information-based hierarchical pooling. It reports the lowest MAE and MSE among listed baselines on DrivAerNet and DrivAerNet++, and transfers to real vehicles with low relative L1 errors and sub-second inference.

  • Problem

    A high-fidelity CFD evaluation typically takes hours to days, making it a costly bottleneck when screening many vehicle design candidates.

    Source: §I · p. 1

  • Method

    HGPTrans predicts drag from vehicle meshes by combining local graph convolutions, Transolver-style global slice attention, and information-score-based hierarchical pooling.

    Source: §I · p. 2, A. Mesh preprocessing and overall… · p. 3

  • Results

    HGPTrans achieves the lowest MAE and MSE among listed baselines on DrivAerNet and DrivAerNet++, with relative L1 errors of 1.56% for sedans and 2.12% for SUVs on the real-vehicle test set.

    Source: §V · pp. 10–11

  • Takeaways & Limitations

    Real-vehicle transfer yields predictions at about 0.293 s per vehicle, several orders of magnitude faster than high-fidelity CFD.

    Source: §V · p. 11

    Evaluation covers steady-state external flow and rigid geometries, while the real-vehicle set is limited to one manufacturer’s production models.

    Source: §V · p. 11

Abstract

from arXiv · show

Accurate and rapid prediction of the aerodynamic drag coefficient ($C_D$) is essential for vehicle design, particularly during early-stage design, where many candidate geometries must be evaluated. Although computational fluid dynamics (CFD) provides reliable aerodynamic estimates, its high computational cost limits large-scale design exploration. This paper proposes the hierarchical graph-pooling Transolver (HGPTrans), which combines hierarchical graph pooling with Transolver-based attention to directly predict $C_D$ from vehicle surface meshes. Motivated by the fact that vehicle aerodynamics depends on both local geometric features and long-range interactions among spatially distant surface regions, HGPTrans integrates three complementary components. Graph isomorphism convolutions encode discriminative local geometry, Transolver-style slice attention captures global interactions with linear computational complexity, and information-redundancy-aware hierarchical pooling progressively removes redundant nodes while preserving informative geometric structures. The model is trained and evaluated on the large-scale DrivAerNet and DrivAerNet++ datasets, where it achieves the lowest mean absolute error and mean squared error among the evaluated baselines. Its generalization capability is further assessed through transfer learning on a real-vehicle dataset containing both sedans and sport utility vehicles (SUVs), achieving relative $L_1$ errors of 1.56\% (sedans) and 2.12\% (SUVs) with an inference time of approximately $0.293$ s per vehicle. This corresponds to an acceleration of several orders of magnitude relative to high-fidelity CFD while keeping the predicted drag coefficients within a few percent of the CFD reference. Ablation studies confirm each component's contribution and reveal the effects of depth and pooling ratio.

I. INTRODUCTION

Vehicle drag prediction matters to energy efficiency and design, but high-fidelity CFD can take hours to days per candidate. HGPTrans combines local geometry encoding, global interaction, and hierarchical graph pooling to predict drag from vehicle meshes.

I. INTRODUCTION

  • Hours to days for one high-fidelity CFD evaluation make screening dozens to hundreds of design candidates a severe bottleneck.The process includes geometry cleanup, mesh generation, numerical solution, and post-processing.Source: §I · p. 1
  • Vehicle drag prediction must preserve local surface details, capture long-range aerodynamic coupling, and remain affordable on production-scale meshes.The challenges include fine geometric features, global interactions among flow regions, and the O(N^2) cost of full attention.Source: §I · p. 2
  • Prior approaches leave gaps in hierarchical mesh coarsening, explicit surface connectivity, or scalar drag regression under strict computational budgets.The cited approaches include single-resolution graph attention, point clouds, and methods focused on flow-field reconstruction.Source: §I · p. 2
  • HGPTrans predicts drag directly from vehicle surface meshes by combining hierarchical graph pooling with Transolver-style slice attention.Its contributions include local graph features, global interaction, redundancy-aware pooling, and transfer learning from DrivAerNet++ to real vehicles.Source: §I · p. 2
  • The evaluation spans DrivAerNet, DrivAerNet++, and a real-vehicle dataset covering sedans and SUVs, with architecture and hyperparameter ablations.The paper also assesses transfer learning on the real-vehicle data.Source: §I · p. 2

II. METHOD

HGPTrans preprocesses vehicle meshes into graph inputs and applies stacked blocks that progressively coarsen the surface representation. Block-level embeddings are combined to regress the drag coefficient.

II. METHOD

  • Meshes are normalized, and high-resolution meshes are simplified with QEM while meshes already at target resolution skip that step.QEM downsampling retains the principal vehicle shape and local surface characteristics.Source: A. Mesh preprocessing and overall… · pp. 2–3
  • Each mesh vertex becomes a graph node, each mesh edge becomes a graph edge, and six input features combine normalized coordinates with surface normals.The task is to map the processed mesh directly to the drag coefficient.Source: A. Mesh preprocessing and overall… · p. 3
  • Stacked HGPTrans blocks alternate local graph convolution, global slice attention, and hierarchical pooling before graph embeddings feed a regression head.Mean and max pooled embeddings from each block are summed and passed to fully connected layers predicting the scalar drag coefficient.Source: A. Mesh preprocessing and overall… · p. 3
  • Progressive coarsening retains fine geometry early and sparser informative locations later, reducing subsequent attention cost while preserving aerodynamic-relevant information.Global attention maintains coupling among regions as the graph becomes coarser.Source: A. Mesh preprocessing and overall… · p. 3

B. Graph convolution with a graph isomorphism network

The method combines sum-aggregation graph convolutions for local surface patterns with slice attention for global aerodynamic interactions. Fixed-size latent slices provide global context with linear complexity in the number of vertices.

B. Graph convolution with a graph isomorphism network

  • GIN uses unnormalized sum aggregation to distinguish local graph structures and preserve neighbor-feature multiplicity that mean or max aggregation can discard.This helps encode sharp transitions such as corners, edges, and curvature discontinuities in aerodynamic-critical regions.Source: B. Graph convolution with a graph… · p. 3
  • GIN combines standardized vertex coordinates and surface normals with mesh topology to form local geometric features for later global attention.The six input channels are projected into a hidden representation before the GIN update.Source: B. Graph convolution with a graph… · p. 3

C. Global interaction with Transolver-style slice attention

  • Slice attention softly assigns vertex features to K learnable slices, attends among their tokens, then broadcasts updated global context back to vertices.The small fixed slice count provides global interaction without full attention over all vertices.Source: C. Global interaction with… · p. 3
  • With fixed K, slice-attention cost is O(KN + K^2), linear in the number of vertices, while alternating GIN and attention refines local and global features across blocks.Local GIN features help form slices, and attention writes global context back to vertices for subsequent local aggregation.Source: C. Global interaction with… · p. 4

D. Hierarchical graph pooling

Hierarchical pooling reduces graph size and builds a multi-scale vehicle representation by selecting vertices according to feature information relative to their neighborhoods. The criterion favors locally distinctive surface features without assuming every retained vertex is aerodynamic-critical.

D. Hierarchical graph pooling

  • Hierarchical pooling progressively reduces vertex count, lowering later-layer cost while inducing a multi-scale representation of the vehicle surface.Its selection criterion uses each vertex’s information content.Source: D. Hierarchical graph pooling · p. 4
  • A vertex’s information score measures the L1 distance between its feature and the mean-aggregated feature of its neighbors; the top rN scores are retained.The retained features and induced adjacency form the coarsened graph.Source: D. Hierarchical graph pooling · p. 4
  • The parameter-free criterion favors less reconstructible vertices near geometric transitions, rather than assuming every retained vertex is aerodynamic-critical.It measures feature redundancy relative to the local neighborhood.Source: D. Hierarchical graph pooling · p. 4

E. Comparison with prior methods

HGPTrans combines graph convolution, global slice attention, and information-driven hierarchical pooling. This combination distinguishes it from methods that lose mesh detail, depend on deep message passing, or omit explicit graph coarsening.

E. Comparison with prior methods

  • HGPTrans uses graph convolution to exploit explicit surface topology, unlike voxel methods that lose detail and point-cloud methods that disregard mesh connectivity.The comparison also notes that voxel-based convolution incurs O(N^3) cost.Source: E. Comparison with prior methods · p. 5
  • A global slice-attention operation captures long-range aerodynamic coupling in one operation, unlike pure message-passing networks that require deep stacks to propagate information.Source: E. Comparison with prior methods · p. 5
  • Information-content-driven hierarchical coarsening reduces computational cost and induces a multi-scale representation, distinguishing HGPTrans from graph-transformer surrogates without explicit coarsening.Source: E. Comparison with prior methods · p. 5

A. Benchmark datasets: DrivAerNet and DrivAerNet++

DrivAerNet and DrivAerNet++ provide CFD-labeled vehicle-design benchmarks with explicit mesh and flow-field data, while the real-vehicle dataset tests applicability across more detailed production geometries.

A. Benchmark datasets: DrivAerNet and DrivAerNet++

  • DrivAerNet contains about 4,000 CFD-labeled vehicle meshes, and DrivAerNet++ expands the collection to about 8,000 designs spanning more body, underbody, and wheel geometries.DrivAerNet includes explicit wheels and underbody, and both datasets provide multiple geometry and flow-field representations.Source: A. Benchmark datasets: DrivAerNet and… · p. 5

B. Real-vehicle dataset

  • The real-vehicle dataset contains 400 schemes—200 sedans and 200 SUVs—with five models per category and C_D values spanning 0.19–0.28.Each surface mesh has about 1 × 10^7 faces and fine components such as front-wheel deflectors and air curtains, making the task more demanding than benchmark prediction.Source: B. Real-vehicle dataset · pp. 5–6
  • Real-vehicle reference flow fields come from steady RANS simulations at a freestream speed of 120 km/h in a full-scale digital reproduction of a CAERI automotive wind tunnel.The modeled domain truncates the closed-return circuit to the contraction, nozzle, test section, collector, diffuser, and downstream extension.Source: B. Real-vehicle dataset · p. 5

C. Data preprocessing

Preprocessing retains benchmark meshes directly but simplifies dense real-vehicle meshes; the experiments then use fixed data splits, specified optimization settings, and transfer learning for real-vehicle prediction.

C. Data preprocessing

  • Real-vehicle meshes are simplified with QEM from about 1 × 10^7 faces to approximately 4 × 10^5 faces before network input, while benchmark meshes are used directly.Coordinates and surface normals form six input channels standardized per mesh; simplification reduces cost and memory while preserving essential body geometry.Source: C. Data preprocessing · p. 6

D. Training and evaluation setup

  • Both datasets use 70:15:15 train-validation-test splits, and the model is trained with MSE and Adam using gradient accumulation over 16 samples.The setup uses four HGPTrans blocks, hidden dimension 256, eight attention heads, 32 slices, and pooling ratio 0.8; inference timing is per vehicle on one L20 GPU, including loading and mesh simplification.Source: D. Training and evaluation setup · p. 6
  • Real-vehicle experiments pre-train on DrivAerNet++ and fine-tune on a small real-vehicle subset to reduce the real-data requirement.Source: D. Training and evaluation setup · p. 6

IV. EXPERIMENTAL RESULTS AND ANALYSIS

HGPTrans reports lower error than available baselines on both benchmark datasets, with particularly strong comparisons against graph-based models on DrivAerNet. It also predicts each DrivAerNet-scale vehicle in about 0.21 seconds on an NVIDIA L20 GPU.

A. Prediction performance on DrivAerNet and DrivAerNet++

  • On DrivAerNet, HGPTrans reports MSE 2.398 × 10−5 and MAE 3.718 × 10−3, both below available baseline values in Table I; its R2 = 0.968 is slightly below TripNet (0.972).Its MAE is reduced by approximately 46% versus RegDGCNN and by more than 48% versus GCNN and PointNet.Source: A. Prediction performance on… · p. 7
  • On DrivAerNet++, HGPTrans reports MSE 5.625 × 10^-5, MAE 5.694 × 10^-3, and maximum absolute error 3.054 × 10^-2, all below available values.Compared with TripNet, its MAE is about 21% lower and MSE about 38% lower; relative L1 and L2 errors are 2.15% and 2.83%.Source: A. Prediction performance on… · p. 7
  • 0.21 s per DrivAerNet-scale vehicle on an NVIDIA L20 is several orders of magnitude shorter than high-fidelity CFD, and 81.2% of DrivAerNet test samples have relative error below 2%.For DrivAerNet++, 56.1% of samples are below 2% relative error; the corresponding below-3% proportions are 94.5% and 75.3%.Source: A. Prediction performance on… · p. 7

B. Transfer learning on the real-vehicle dataset

The section evaluates transfer from DrivAerNet++ to real vehicles by fine-tuning one model on simplified meshes. It reports improved results over training from scratch and frames predictions as an early-screening aid, not a replacement for final CFD validation.

B. Transfer learning on the real-vehicle dataset

C. Ablation studies

The ablations compare the full HGPTrans model with variants that alter individual modules or input features. They report accuracy degradation when components or surface normals are removed and examine block depth and pooling ratio against error and inference time.

1. Architecture ablation

  • Replacing GIN raised MAE from 3.718 × 10−3 to 3.781×10−3 with GCN and 3.938 × 10−3 with an MLP.Source: §1 · p. 9, Table III · p. 10
  • Removing Transolver attention reduced parameters from 2.490 million to 0.628 million but increased MSE by 3.5%, from 2.398 × 10−5 to 2.481 × 10−5.Source: §1 · p. 9, Table III · p. 10
  • Removing hierarchical pooling increased MAE from 3.718 × 10−3 to 4.021×10−3; the authors also report that coarsening reduces nodes processed by later blocks.Source: §1 · pp. 9–10, Table III · p. 10
  • The hyperparameter ablation varies block count L and pooling ratio r, tracking mean absolute error and inference time.Source: Figure 6 · p. 10
  • Removing surface normals increased MAE to 4.153×10−3, the largest degradation among the reported ablations.Source: §1 · p. 10, Table III · p. 10

2. Hyperparameter ablation

The hyperparameter sweep identifies depth and pooling settings that balance prediction accuracy with inference cost. The ablations support the selected architectural components.

2. Hyperparameter ablation

  • 3.718×10−3 MAE is reached at L = 4, while adding a fifth block raises MAE to 3.921 × 10−3.Inference time increases from 0.179 s at L = 1 to 0.230 s at L = 5; L = 4 is selected as a balance between accuracy and computational cost.Source: §2 · p. 10
  • At r = 0.8, MAE is 3.718×10−3 at 0.210 s/sample; r = 0.3 and 0.9 raise MAE to 4.875×10−3 and 4.856×10−3, respectively.r = 0.3 discards aerodynamic-critical features, while r = 0.9 has the sweep's highest inference cost at 0.246 s per sample.Source: §2 · p. 10
  • Sum-aggregation graph convolution, global slice attention, information-score pooling, and surface normals each contribute to accuracy; hierarchical coarsening also reduces computational cost.Removing Transolver attention degrades accuracy despite reducing the parameter count to 0.63 million, while removing pooling increases error despite changing parameter count only slightly.Source: §2 · p. 10

V. CONCLUSIONS

HGPTrans predicts automotive drag coefficients from vehicle surface meshes and achieves the lowest listed MAE and MSE on DrivAerNet and DrivAerNet++. Transfer learning also yields reported results on sedans and SUVs, with the conclusion noting limits in flow conditions and vehicle scope.

V. CONCLUSIONS

  • HGPTrans achieves the lowest MAE and MSE among listed DrivAerNet and DrivAerNet++ baselines, using approximately 2.490 million parameters.The model combines graph isomorphism convolution, Transolver-style slice attention, and information-score-based hierarchical pooling.Source: §V · p. 10
  • The model is evaluated on steady-state external flow and rigid geometries, not transient yaw or crosswind conditions; real-vehicle evaluation covers one manufacturer's production models.Generalization to active aerodynamic components remains to be investigated.Source: §V · p. 11

DECLARATIONS

  • DrivAerNet and DrivAerNet++ are openly available, but the real-vehicle dataset is proprietary and confidential; the source code is public.The real-vehicle dataset cannot be shared.Source: DECLARATIONS · p. 11

Related papers

Loading 2609.31765v2…