File size: 4,437 Bytes
bdce880 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | # Transolver for PDE Solving
We evaluate [Transolver](https://arxiv.org/abs/2402.02366) with six widely used PDE-solving benchmarks, which is provided by [FNO and GeoFNO](https://github.com/neuraloperator/neuraloperator).
**Transolver achieves 22% averaged relative promotion over the previous second-best model, presenting favorable efficiency and scalibility.**
<p align="center">
<img src=".\fig\standard_benchmark.png" height = "300" alt="" align=center />
<br><br>
<b>Table 1.</b> Comparison in six standard benchmarks. Relative L2 is recorded.
</p>
## Get Started
1. Install Python 3.8. For convenience, execute the following command.
```bash
pip install -r requirements.txt
```
2. Prepare Data. You can obtain experimental datasets from the following links.
| Dataset | Task | Geometry | Link |
| ------------- | --------------------------------------- | --------------- | ------------------------------------------------------------ |
| Elasticity | Estimate material inner stress | Point Cloud | [[Google Cloud]](https://drive.google.com/drive/folders/1YBuaoTdOSr_qzaow-G-iwvbUI7fiUzu8) |
| Plasticity | Estimate material deformation over time | Structured Mesh | [[Google Cloud]](https://drive.google.com/drive/folders/1YBuaoTdOSr_qzaow-G-iwvbUI7fiUzu8) |
| Navier-Stokes | Predict future fluid velocity | Regular Grid | [[Google Cloud]](https://drive.google.com/drive/folders/1UnbQh2WWc6knEHbLn-ZaXrKUZhp7pjt-) |
| Darcy | Estimate fluid pressure through medium | Regular Grid | [[Google Cloud]](https://drive.google.com/drive/folders/1UnbQh2WWc6knEHbLn-ZaXrKUZhp7pjt-) |
| AirFoil | Estimate airflow velocity around airfoil | Structured Mesh | [[Google Cloud]](https://drive.google.com/drive/folders/1YBuaoTdOSr_qzaow-G-iwvbUI7fiUzu8) |
| Pipe | Estimate fluid velocity in a pipe | Structured Mesh | [[Google Cloud]](https://drive.google.com/drive/folders/1YBuaoTdOSr_qzaow-G-iwvbUI7fiUzu8) |
3. 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
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.
4. 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]](https://en.wikipedia.org/wiki/Shock_wave) around airfoil.
<p align="center">
<img src=".\fig\showcase.png" height = "400" alt="" align=center />
<br><br>
<b>Figure 1.</b> Case study of different models.
</p>
## 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.
<p align="center">
<img src=".\fig\scalibility.png" height = "200" alt="" align=center />
<br><br>
<b>Figure 2.</b> Scaling up Transolver: relative L2 curve w.r.t. model layers.
</p>
## 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](mailto: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
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