HGPTrans: Hierarchical Graph-Pooling Transolver for Vehicle Drag Prediction

Official PyTorch implementation of HGPTrans: hierarchical graph-pooling Transolver for vehicle aerodynamic drag prediction (Cd regression) from STL meshes.

Predict the aerodynamic drag coefficient (Cd) of a vehicle directly from its surface mesh. The model builds a graph from the triangle mesh (vertices + normals as node features, mesh edges as the graph edge set), runs GIN message passing, applies Transolver-style physics attention over learned slice tokens (suited to irregular meshes), and performs hierarchical TopK graph pooling with a multi-scale pooled readout.

├── models.py        # HGPTrans model (GIN message passing + physics attention)
├── dataset.py       # STL mesh-graph dataset + per-sample standardization
├── train.py         # DDP training loop (gradient accumulation, checkpointing)
├── evaluate.py      # Test-split / extra-STL evaluation with metrics
├── utils.py         # logging, label lookup, seeding, plotting helpers
├── requirements.txt

Requires Python 3.9+ and CUDA (for training on GPU).

git clone https://github.com/BoLiu-USTC/HGPTrans.git
cd HGPTrans
pip install -r requirements.txt

torch and torch_geometric are listed but their CUDA-matched wheels depend on your local CUDA version, so install them first following the official guides if the pinned wheels do not match your driver:

• PyTorch: https://pytorch.org/get-started/locally/
• PyG: https://pytorch-geometric.readthedocs.io/en/latest/install/installation.html

Point --data_dir at a dataset directory with this layout (DrivAerNet / DrivAerNet++ style):

data_dir/
├── cleaned_stls/               # one <design_id>.stl per design
├── labels.xlsx                 # columns: ID, Drag_Value
└── train_val_test_splits/
    ├── train_design_ids.txt    # one design id per line
    ├── val_design_ids.txt
    └── test_design_ids.txt

The DrivAerNet++ 8k+ variant (train.txt / val.txt / test.txt splits and DrivAerNetPlusPlus_Cd_8k_Updated.xlsx) is auto-detected as well.

# single GPU
python train.py --data_dir /path/to/DrivAerNet++ --save_dir ./logs/run1

# multi GPU (DDP)
python train.py --data_dir /path/to/DrivAerNet++ --save_dir ./logs/run1 --world_size 4

# resume from <save_dir>/checkpoint.pth
python train.py --data_dir /path/to/DrivAerNet++ --save_dir ./logs/run1 --resume

Key options: --accumulation_steps (default 16, i.e. effective batch = batch_size × accumulation_steps = 16 × 1). Vertex features are standardized per sample (zero mean / unit variance over each mesh).

# on the dataset test split
python evaluate.py --data_dir /path/to/DrivAerNet++ \
    --checkpoint ./logs/run1/model_best.pt

# on a folder of extra STL files whose names encode the true Cd,
# e.g. design_0.312.stl -> truth Cd = 0.312
python evaluate.py --data_dir /path/to/DrivAerNet++ \
    --checkpoint ./logs/run1/model_best.pt --extra_data ./data/Ahmed

Per-design predictions are written to predLog/preds.txt next to the checkpoint; metrics (MSE / MAE / R² / rel-L2 / Pearson / Spearman) are printed and an error-scatter plot is saved to predLog/error.png.

• Keep --batch_size 1: model forwards use dense reshapes that assume a single graph per batch. Use --accumulation_steps for larger effective batches.
• All meshes above --simplify_size vertices (default 417,114) are decimated with quadric edge collapse before graph construction.
• Training latency printed during validation is forward-only; the end-to-end per-car inference time (mesh loading + QEM decimation + forward) reported in the paper is measured over the full pipeline.

The accompanying paper is available on arXiv:2609.31765.

If you use this code or method, please cite:

@article{liu2026hgptrans,
  title        = {HGPTrans: Hierarchical Graph-Pooling Transolver for Automotive Aerodynamic Drag Coefficient Prediction},
  author       = {Liu, Bo and Zhang, Fengli and Luo, Qiuli and Nie, Lianrui and Wang, Wenjiang},
  journal      = {arXiv preprint arXiv:2609.31765},
  year         = {2026},
  url          = {https://arxiv.org/abs/2609.31765}
}

Released under the MIT License.