Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis

Bartłomiej Borzyszkowski · Karol Damaszke · Jakub Romankiewicz · Marcin Świniarski · Marek Moszyński

Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology
ul. G. Narutowicza 11/12, 80-233 Gdańsk, Poland

Experimental-PGNNs

In this project, we present two applications of Physics-Guided Neural Networks (PGNN) and illustrate their advantages in theory by solving Poisson’s and Burger’s partial differential equations. The proposed formulas describe various real-world processes and are widely used in the area of applied mathematics.

Setup

• Install Python 3.6.7+ if not present on machine: https://www.python.org/downloads/release/python-367/
• Install virtualenv: pip install virtualenv
• Create venv environment: python -m venv
• Activate venv:
  • using Windows: venv\Scripts\activate.bat
  • using Linux: source venv/bin/activate
• Install requirements: pip install -r requirements.txt
• Run jupyterlab: jupyter lab
• Open the jupyter in the browser and work on the notebooks

Contact

• Email: [email protected]

Citation

Please cite our work as follows:

@article{borzyszkowski2021physics,
  title={Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis},
  author={Borzyszkowski, Bartlomiej and Damaszke, Karol and Romankiewicz, Jakub and Swiniarski, Marcin and Moszynski, Marek},
  journal={Bulletin of the Polish Academy of Sciences. Technical Sciences},
  volume={69},
  number={6},
  year={2021}
}