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

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

cs.CVSep 24, 2026

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

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

Organizations: Institute of Auto Engineering, BYD Auto Industry Co., Ltd., Shenzhen, China

Abstract

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.

Figures & tables

Figure 1: The overall architecture of HGPTrans. The input vehicle meshes are first normalized, and high-resolution meshes are simplified using QEM to obtain downsampled meshes. The processed mesh is converted into a graph and passed through the stacked HGPTrans blocks, graph-level pooling, and fully connected layers to predict the drag coefficient $C_{D}$ .

Figure 2: Comparison of representative vehicle geometries from the DrivAerNet open-source dataset and the real-vehicle dataset (a production sedan). The real-vehicle geometries contain a substantially higher level of geometric detail.

Figure 3: Computational domain of the full-scale digital wind tunnel.

Dataset	Model	MSE ( $10^{-5}$ ) $\downarrow$	MAE ( $10^{-3}$ ) $\downarrow$	MaxAE ( $10^{-2}$ ) $\downarrow$	$R^{2}$ $\uparrow$
	HGPTrans	2.398	3.718	1.936	0.968
	TripNet	2.602	4.030	1.268	0.972
	FIGConvNet	3.225	4.423	2.134	0.957
	PointNeXt	4.577	5.200	2.410	0.939
	ASSANet	5.433	5.810	2.390	0.927
	MeshGraphNets	6.000	6.080	2.965	0.917

Table 1: Comparison of HGPTrans with mainstream baseline models on the DrivAerNet and DrivAerNet++ datasets. The best value within each dataset block is highlighted in bold. Baseline entries are taken from the cited literature and use the splits reported by the respective sources.

Figure 4: Scatter plots of the predicted versus the ground-truth drag coefficient on the test sets of (a) DrivAerNet and (b) DrivAerNet++. The dashed line indicates the ideal $y=x$ diagonal.

Figure 5: (a) Scatter plot of the predicted versus the ground-truth drag coefficient on the real-vehicle test set; the inset reports the coefficient of determination for the sedan and SUV subsets. (b) Scatter plot of the predicted versus the ground-truth difference $\Delta C_{D}$ for all pairs of variants within the sedan and SUV subsets; blue and red markers denote the pairs for which the model predicts the direction of the change correctly and incorrectly, respectively, and the inset reports the direction accuracy for each subset.

With transfer learning (pre-trained on DrivAerNet++)
Subset	MSE ( $10^{-5}$ ) $\downarrow$	MAE ( $10^{-3}$ ) $\downarrow$	MaxAE ( $10^{-2}$ ) $\downarrow$	Rel. $L_{1}$ ( $\%$ ) $\downarrow$	Rel. $L_{2}$ ( $\%$ ) $\downarrow$	$R^{2}$ $\uparrow$
Total	3.152	4.267	1.826	1.865	2.441	/
Sedan	2.311	3.227	1.826	1.555	2.314	0.770
SUV	3.993	5.306	1.656	2.123	2.524	0.816
Without transfer learning (trained from scratch on the real-vehicle data)
Total	5.549	5.341	3.405	2.335	3.238	/

Table 2: The results of HGPTrans on the real-vehicle dataset, evaluated on the held-out test set and reported for the total test set and the sedan and SUV subsets. The upper block corresponds to the proposed transfer-learning setting (pre-trained on DrivAerNet++); the lower block is a baseline trained from scratch on the real-vehicle data only.

Variant	MSE ( $10^{-5}$ )	MAE ( $10^{-3}$ )	$R^{2}$	Param. ( $10^{6}$ )
Full HGPTrans	2.398	3.718	0.968	2.490
GIN $\rightarrow$ GCN	2.445	3.781	0.967	2.226
GIN $\rightarrow$ MLP	2.635	3.938	0.965	2.490
w/o Transolver	2.481	3.820	0.967	0.628
w/o pooling	2.726	4.021	0.964	2.488
w/o normal features	2.866	4.153	0.962	2.489

Table 3: Architecture ablation study on DrivAerNet. The full model is compared with variants in which the local convolution, the global attention, the pooling, and the input features are modified.

Figure 6: Hyperparameter ablation on DrivAerNet: (a) effect of the number of HGPTrans blocks $L$ and (b) effect of the pooling ratio $r$ on the mean absolute error and the inference time.

Explore similar work

A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction
Jun 5, 2026Kangkang Qi, Huiyu Yang, Keqi Ding +5PDE Surrogate Modeling Computational Fluid Dynamics
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Tenfong Technology Co., Ltd., Shenzhen 518000, China +1
Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD
Apr 20, 2026Nicholas Thumiger, Andrea Bartezzaghi, Mattia Rigotti +5PDE Surrogate Modeling Neural Operators
IBM Research · Dallara Automobili
RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics
Apr 30, 2026Bojun Zhang, Huiyu Yang, Yunpeng Wang +4Rotary Positional Embeddings PDE Operator Learning
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China · Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology,Shenzhen 518055, China · Ningbo Key Laboratory of Advanced Manufacturing Simulation, Eastern Institute of Technology, Ningbo, 315200, China +1

Jun 5, 2026, cs.LGJ/K move · Enter open · S save

A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction

Kangkang Qi, Huiyu Yang, Keqi Ding, Yunpeng Wang+4

Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology, Shenzhen 518055, China · Shenzhen Tenfong Technology Co., Ltd., Shenzhen 518000, China+1

PDE Surrogate Modeling Computational Fluid Dynamics

Open paper AskPDF arXiv

High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration. Machine-learning-based surface-field prediction offers a faster alternative if the model can efficiently capture both global flow context and local geometric detail. This work proposes a machine-learning-based method, named the geometry-aware triplane field network (GTF-Net), for vehicle aerodynamic pressure and wall shear stress prediction. GTF-Net constructs triplane features directly from sampled surface points through a shared multilayer perceptron (MLP) and smooth bilinear rasterization. The planes are then processed by a dual-stream backbone that combines adaptive Fourier neural operator (AFNO) spectral mixing with convolutional neural network (CNN) refinement, so long-range aerodynamic coupling and local geometry-induced variations are modeled in the same representation. At query stage, sampled triplane features are combined with vehicle-aligned directional coordinates, normal-projection features, and a voxel-based curvature proxy. GTF-Net is compared with Transolver, geometry-informed neural operator (GINO), and TripNet, a triplane-based surrogate model. GTF-Net improves the relative L2 error from the strongest baseline value of 0.157 to 0.145 for pressure prediction and from 0.237 to 0.226 for wall shear stress prediction. Ablation results show that AFNO mixing, local CNN refinement, and query-side geometric encoding each contribute to accuracy, supporting the proposed mechanism of combining structured triplane representation with explicit aerodynamic geometry cues.

Abstract

Explore similar work

A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction

Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics