PDE-Net

This is the code for the paper

PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
Long Zichao, Lu Yiping, Dong Bin

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

@article{long2019pde,
  title={PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network},
  author={Long, Zichao and Lu, Yiping and Dong, Bin},
  journal={Journal of Computational Physics},
  pages={108925},
  year={2019},
  publisher={Elsevier}
}

Setup

All code were developed and tested on CentOS 7 with Python 3.7, and were implemented by pytorch 1.1.0

The code are based on A PyTorch Extension for Applied Mathematics aTEAM. The easiest way to download a proper version of aTEAM for PDE-Net 2.0 is to use git submodule tools.

For example, you can create a conda environment and set up PDE-Net 2.0 like this:

conda create -n PDE-Net-2 python=3.7 scipy pyyaml jupyter matplotlib
source activate PDE-Net-2
conda install pytorch=1.1 torchvision cudatoolkit=9.2 -c pytorch
git clone [email protected]:ZichaoLong/PDE-Net.git
cd PDE-Net
git checkout PDE-Net-2.0 # switch your branch from 'master' to the 'PDE-Net-2'
git submodule init
git submodule update

In addition, insead of applying PDE-Net (2.0) directly to your own problems, we recommand you to build your own codes upon the basic extension library aTEAM for further reseach.

Usage

Model	example of config file
Burgers' Equation	checkpoint/burgers-noise0.001/options.yaml
Diffusion Equation	checkpoint/heat-noise0.001/options.yaml
Reaction Convection Diffusion Equation	checkpoint/cdr-noise.0.001/options.yaml

The following documents are mainly take Burgers' equation for explaining. The usage for diffusion equation and CDR (convection diffusion with reactive source) equation is similar to Burgers' equation (Change dataname='burgers' to dataname='heat' or dataname='cdr').

Training

• Default options can be found in conf.py, see conf.default_options.

• Method1: Configure training by command line options (terminal interface):

dataname="burgers"
constraint=2
kernel_size=5
stablize=0
sparsity=0.005
scheme=upwind
momentsparsity=0.001
viscosity=0.05
noise=0.001
data_start_time=1
hidden_layers=5
casename=${dataname}-${constraint}-${scheme}-sparse${sparsity}-noise${noise}
python train.py \
    --name=${casename} \
    --dataname=$dataname --constraint=${constraint} --device=cuda:0 \
    --kernel_size=${kernel_size} --viscosity=${viscosity} --blocks=0-6,9 \
    --start_noise=${noise} --end_noise=${noise} \
    --stablize=${stablize} --sparsity=${sparsity} --momentsparsity=${momentsparsity} \
    --data_start_time=${data_start_time} --dt=1e-2 --max_dt=1/1600

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

• Method2: Retrain an existing case for more blocks, and start from block 9:

N=3
python train.py --name=${casename} --configfile=checkpoint/${casename}/options.yaml \
    --start_from=${N} --blocks=12,15,18,21,24,27,30,35,40

• Method3: Configure your case first and then train it:

cp -r checkpoint/burgers-noise0.001 checkpoint/test
# modify checkpoint/test/options.yaml and then exit
python train.py --name=test --configfile=checkpoint/test/options.yaml

• For more examples about training please refer to ${dataname}job.slurm,${dataname}manytrain.slurm, where dataname=burgers or heat or cdr

Test

We should generate data first before we test the learned model. ./burgersdatafortest.slurm will generate test data according to the default configuration file checkpoint/burgers-noise0.001/options.yaml. Please change this parameter in burgersdatafortest.slurm if needed. NOTICE: Please make sure your configuration of the test data is as the same as your learned model. Then test your learned case:

for ((i=0;i<20;i++)) do
    # test on i-th batch of test data and store the results in checkpoint/$casename
    python _test.py $casename $i
done
# aggregate errors of 20 batches of test data, remove tmporary results
python test.py $casename 20

Then the testing results will be stored in checkpoint/$casename/errs. See burgerscompareerrs.py to visualize your results.

TIPS: Try to run ./burgersdatafortest.slurm; ./burgersjob.slurm; ./burgerserrs.slurm in a workstation with 4 GPUs.

Learn more details about your trained model

We highly recommand you to refer to ${dataname}debug.py, and run the code line by line in an interactive python IDE (e.g. Jupyter Notebook or IPython). You can set your options term by term (include parameters of symnet), load a trained model, print coefficient of SymNet.