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Deep learning library for learning Green's functions

Project description

GreenLearning

Documentation Status

GreenLearning is a deep learning library based on Tensorflow for learning Green's functions associated with partial differential operators.

laplace_rational.png
Exact and learned Green’s function of the Laplace operator..

Below is an example of the Green's function of a second-order differential operator with variable coefficients learned by GreenLearning.

laplace_rational.png
Learned Green’s function of a second order ODE with variable coefficients.

See https://greenlearning.readthedocs.io/en/latest/gallery.html for more examples.

The library is maintained by Nicolas Boullé. If you are interested in using it, do not hesitate to get in contact with him at boulle@maths.ox.ac.uk.

Documentation: ReadTheDocs

Features

  • GreenLearning learns Green's functions and homogeneous solutions associated with scalar and systems of linearized partial differential equations in 1D and 2D with deep learning.
  • Rational neural networks are implemented and used to increase the accuracy of the learned Green's functions.
  • GreenLearning requires no hyperparameter tuning to successfully learn Green's functions.
  • The neural networks can be created and trained easily with a few lines of code.
  • It is simple to generate the training datasets with MATLAB scripts.

Installation

Requirements

GreenLearning relies on the following Python libraries:

How to install GreenLearning

  • For users, you can install the stable version with pip:
pip install greenlearning

or with conda:

conda install -c conda-forge greenlearning
  • For developers, you should clone the GitHub repository and install it manually on your machine::
git clone https://github.com/NBoulle/greenlearning.git
cd greenlearning
pip install -e.

Citation

Please cite the following papers if you are using GreenLearning.

  • About GreenLearning:
@article{boulle2021data,
title={Data-driven discovery of physical laws with human-understandable deep learning},
author={Boull{\'e}, Nicolas and Earls, Christopher J. and Townsend, Alex,
journal={arXiv preprint arXiv:},
year={2021}
}
  • About Rational neural networks:
@inproceedings{boulle2020rational,
title={Rational neural networks},
author={Boull{\'e}, Nicolas and Nakatsukasa, Yuji and Townsend, Alex},
booktitle = {Advances in Neural Information Processing Systems},
volume = {33},
pages = {14243--14253},
year={2020},
url = {https://proceedings.neurips.cc/paper/2020/file/a3f390d88e4c41f2747bfa2f1b5f87db-Paper.pdf}
}

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