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PDE-Solving-StandardBenchmark

README.md

Transolver for PDE Solving

We evaluate Transolver with six widely used PDE-solving benchmarks, which is provided by FNO and GeoFNO.

Transolver achieves 22% averaged relative promotion over the previous second-best model, presenting favorable efficiency and scalibility.



Table 1. Comparison in six standard benchmarks. Relative L2 is recorded.

Get Started

  1. Install Python 3.8. For convenience, execute the following command.
pip install -r requirements.txt
  1. Prepare Data. You can obtain experimental datasets from the following links.
Dataset Task Geometry Link
Elasticity Estimate material inner stress Point Cloud [Google Cloud]
Plasticity Estimate material deformation over time Structured Mesh [Google Cloud]
Navier-Stokes Predict future fluid velocity Regular Grid [Google Cloud]
Darcy Estimate fluid pressure through medium Regular Grid [Google Cloud]
AirFoil Estimate airflow velocity around airfoil Structured Mesh [Google Cloud]
Pipe Estimate fluid velocity in a pipe Structured Mesh [Google Cloud]
  1. Train and evaluate model. We provide the experiment scripts of all benchmarks under the folder ./scripts/. You can reproduce the experiment results as the following examples:
bash scripts/Transolver_Elas.sh # for Elasticity
bash scripts/Transolver_Plas.sh # for Plasticity
bash scripts/Transolver_NS.sh # for Navier-Stokes
bash scripts/Transolver_Darcy.sh # for Darcy
bash scripts/Transolver_Airfoil.sh # for Airfoil
bash scripts/Transolver_Pipe.sh # for Pipe

Note: You need to change the argument --data_path to your dataset path.

  1. Develop your own model. Here are the instructions:

    • Add the model file under folder ./models/.
    • Add the model name into ./model_dict.py.
    • Add a script file under folder ./scripts/ and change the argument --model.

Visualization

Transolver can handle PDEs under various geometrics well, such as predicting the future fluid and estimating the [shock wave] around airfoil.



Figure 1. Case study of different models.

PDE Solving at Scale

To align with previous model, we only experiment with 8-layer Transolver in the main text. Actually, you can easily obtain a better performance by scaling up Transolver. The relative L2 generally decreases when we adding more layers.



Figure 2. Scaling up Transolver: relative L2 curve w.r.t. model layers.

Citation

If you find this repo useful, please cite our paper.

@inproceedings{wu2024Transolver,
  title={Transolver: A Fast Transformer Solver for PDEs on General Geometries},
  author={Haixu Wu and Huakun Luo and Haowen Wang and Jianmin Wang and Mingsheng Long},
  booktitle={International Conference on Machine Learning},
  year={2024}
}

Contact

If you have any questions or want to use the code, please contact wuhx23@mails.tsinghua.edu.cn.

Acknowledgement

We appreciate the following github repos a lot for their valuable code base or datasets:

https://github.com/neuraloperator/neuraloperator

https://github.com/neuraloperator/Geo-FNO

https://github.com/thuml/Latent-Spectral-Models