Data processing

Location: diffice_jax/data

This folder provides the codes that conduct the pre-preprocessing of the input data, including the normalization, flattening and random sampling, and the post-processing of the neural network output, including re-normalization and reshaping. Two versions of codes are provided in this folder. The pinns subfolder involves the code is for the regular PINNs training, and the xpinns subfolder is for the extended-PINNs (XPINNs) training.

The mathematical formation for the regular PINNs training is provided in this link, and the description of the XPINNs setting is given in this link. Both the pinns and xpinns folders contain four Python scripts, each specifying a key component for PINN training. Detailed instructions for correctly calling the functions in these scripts can be found in the example codes within the examples folder of this repository.

/pinns/preprocessing.py & /xpinns/preprocessing.py

Involving essential functions to normalize the raw data loaded from the MATLAB format (.mat). The function in the script will automatically detect the characterisitc scale of each variable in the dataset, including the spatial coordiates \((x,y)\), velocity \((u, v)\) and thickness \(h\), and use them to normalize those variables to be within the range of \([-1, 1]\). The script also re-organizes and reshapes the data that is required by the code in the model folder to ensure the success of the PINN training.

/pinns/sampling.py & /xpinns/sampling.py

Involving essential functions to sample a batch of pre-processed data used for the PINN training. Users can specify the number of sampling points for both velocity and thickness data, as well as the collocation points used to compute equation residue and boundary condition residue in each batch. Note that for the sampling function in the xpinns folder, the number of sampling points specified by users is for each sub-region, not the entire domain.