PDE-Net

This is the code for the paper

PDE-Net: Learning PDEs from Data (ICML 2018)
Long Zichao, Lu Yiping, Ma Xianzhong and Dong Bin

If you find this code useful in your research then please cite

@inproceedings{long2018pde,
    title={PDE-Net: Learning PDEs from Data},
    author={Long, Zichao and Lu, Yiping and Ma, Xianzhong and Dong, Bin},
    booktitle={Proceedings of the 35th International Conference on Machine Learning (ICML 2018)},
    year={2018}
}

Setup

All code was developed and tested on CentOS 7 with Python 3.6, the code is implemented by pytorch 0.3.1

The code is based on aTEAM, a pyTorch Extension for Applied Mathematics, download a proper version of this package, and extract to your python path as aTEAM

For example, you can create a conda environment and run the code like this:

conda create -n pdenet python=3 jupyter
source activate pdenet
pip install scipy
pip install http://download.pytorch.org/whl/cu90/torch-0.3.1-cp36-cp36m-linux_x86_64.whl
# change ".../cu90/..." to ".../cpu/..." or ".../cu91/..." if needed
git clone git@github.com:ZichaoLong/PDE-Net.git
cd PDE-Net
wget https://github.com/ZichaoLong/aTEAM/archive/v0.1.tar.gz
tar -xf v0.1.tar.gz
mv aTEAM-0.1 aTEAM

Training, Testing and Plot

Model	example of config file	training	testing	plot
Convection-Diffusion Equations	checkpoint/linpde.yaml	learn_variantcoelinear2d.py	linpdetest.py	linpdeplot.py
Diffusion Equations with Nonlinear Source	checkpoint/nonlinpde.yaml	learn_singlenonlinear2d.py	nonlinpdetest.py	nonlinpdeplot.py

Training

Default options can be found in learn_variantcoelinear.py and lear_singlenonlinear2d.py. You can simply modify the default options in learn_variantcoelinear.py(lear_singlenonlinear2d.py), and simply run code like:

python learn_variantcoelinear2d.py

Configure training by command line options:

export TASKDESCRIPTOR=linpde-test
python learn_variantcoelinear2d.py --taskdescriptor=$TASKDESCRIPTOR \
  --kernel_size=7 --max_order=4 --constraint=moment

Training information and learned parameters will be stored in checkpoint/${TASKDESCRIPTOR}.

Testing

python linpdetest.py $TASKDESCRIPTOR
# or python nonlinpdetest.py $TASKDESCRIPTOR

Then testing results will be stored in checkpoint/$TASKDESCRIPTOR/errs.pkl.

Show Results

Set your TASKDESCRIPTOR in *test.py, *plot.py, errs_compare.py and run.

Pretrained Model

Download pretrained models and make your working directory like this:

PDE-Net/
  aTEAM/
  figures/
  learn_variantcoelinear2d.py
  linpdetest.py
  ...
  checkpoint/
      linpde5x5frozen4order0.015dt0.015noise-double/
      linpde5x5moment4order0.015dt0.015noise-double/
      linpde7x7frozen4order0.015dt0.015noise-double/
      linpde7x7moment4order0.015dt0.015noise-double/
      nonlinpde7x7frozen2order-double/
      nonlinpde7x7moment2order-double/

2prime / PDE-Net