Physics-informed Fourier Feature GANs (PIFFGANs)

Author: Deep Ray, USC

Date: June 6, 2021

This python script is written to train WGANS with PDE-based constraints.

Setting up a virtual environment

These are the instructions to set up a virtual environment using virtualenv or anaconda and install the following packages:

• tensorflow (or tensorflow-gpu if you plan to use a GPU)
• matplotlib
• pandas
• seaborn

The setup

Currently, the code is setup for a two-dimensional parametrized PDE. See "discription" for details of the models used.

Currently, the code can make use of the following PDEs (set using the --pde_type parameter)

• 'None': No PDE is used, the data is treated as images.
• 'LinAdv': Viscous linear advection.
• 'Burgers': Viscous Burgers equation.

The PDE residual constraints are described in Train/pde_utils.py, which returns a list of residuals associated with the PDE.

Create you own data

To create your own dataset (from a PDE or otherwise), you need to create the following Numpy arrays and save it to a directory (preferably a sub-directory in Data)

• x1.npy: Array of size $$N_1$$, containing the node locations in the $$x_1$$ coordinate directions.
• x2.npy: Array of size $$N_2$$, containing the node locations in the $$x_2$$ coordinate directions.
• u_data.npy: Array of size $$N \times N_1 \times N_2$$, where $$N$$ is the number of samples.
• u_mean.npy: Array of size $$N_1 \times N_2$$ containing the sample mean at each node in the grid.
• u_std.npy: Array of size $$N_1 \times N_2$$ containing the sample standard deviation at each node in the grid.

If the you plan to use a new type of PDE, then after creating the above numpy arrays

• Add a new PDE type choice to the --pde_type argument in Train/config.py
• Add the list of PDE constraints for this new PDE in Train/pde_utils.py. Don't foget to augment the pde type to the function pde_constraints.

Try a quick test

Activate your virtual environment. First create a sample data set by running the following from within the Data directory:

and try running the following from within the Train/Burgers directory:

python3 trainer.py \
        --Nx1_frac=128 \
        --Nx2_frac=128 \
        --Tfinal=0.2 \
        --Nu=10000 \
        --Nu_save=1000 \
        --ictype=SineExp \
        --base_params 0.8 0.0 0.1 0.1
        --visc=0.01

Have a look at the data file created in Train/Burgers/SineExp. Next, go to the Train directory and run the following command to train a network

python3 trainer.py \
        --data_dir=../Data/Burgers/SineExp \
        --Nx1_frac=0.1 \
        --Nx2_frac=0.1 \
        --g_type='FF' \
        --g_width=100 \
        --d_type='CNN' \
        --d_width=100 \
        --n_epoch=200 \
        --pde_type=Burgers \
        --z_dim=5 \
        --pde_params 0.0 \
        --pdecon_coef 0.0 \
        --batch_size=50 \
        --savefig_freq=10 \
        --Nu=200 \
        --save_dir=Results

The training results and checkpoints will be saved in xps/Results