Accuracy-and-Robustness-of-Weight-Balancing-Methods-for-Training-PINNs

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Accuracy-and-Robustness-of-Weight-Balancing-Methods-for-Training-PINNs

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# Accuracy-and-Robustness-of-Weight-Balancing-Methods-for-Training-PINNs

# Installation

Create a virtual environment running on Python 3.12. Install the requirements:
```
pip install -r requirements.txt
```

# Run the code

Each example can be run independently:
* One-dimensional quasi-linear hyperbolic equation: in the `Godunov` folder, the main file is `main_godunov.py`. For the analysis, one can use the `loss_landscape.ipynb` jupyter notebook.
* The Helmholtz equation: in the `Helmholtz` folder, the main file is `main_helmholtz.py`.
* One-dimensional Poisson equation: in the folder `Poisson`, the main file is `main_poisson.py`.

# Licence

The project is under the MIT licence. See the [terms](./LICENSE) for more details.

# How to cite this project

This GitHub repository is related to the article: Barreau, M., & Shen, H. (2025). _Accuracy and Robustness of Weight-Balancing Methods for Training PINNs_. **arXiv preprint** arXiv:2501.18582.

To cite the project in your paper via BibTex:
```
@article{barreau2025accuracy,
  title={Accuracy and Robustness of Weight-Balancing Methods for Training {PINNs}},
  author={Barreau, M. and Shen, H.},
  journal={arXiv preprint arXiv:2501.18582},
  year={2025}
}
```

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