Physics Informed Convex Artificial Neural Networks

This repository contains the source code used for the work in \cite{}. It allows to train a PICANN network to learn the optimal transport map between a unknown target distribution and a reference distribution. The transport map then can be applied on the reference distribution to get the density estimation of the unknown distribution. The inverse map can be used to transform the samples from reference distribution to generate new samples from the target distribution.

More details can be found in the article below.

Will be added

Python 3.6 Numpy >= 1.19.1 Pytorch >= 1.6.0 Scipy >= 1.5.0 Matplotlib >= 3.2.2

To run experiments in Table 1 : Run the bash script "Run_Tbl1_Exp.sh" with the appropriate parameters. The script assumes there are 2 GPUs to run 10 experiments each. If not change the parameters in the script.

To generate Fig 3 and Fig 4 : Run the python script "PICANN_Example_Script.py" with appropriate dataset. After the training is done. Use another script "Make_Results.py" to generate all the graphs.

Once we have a forward model trained on any dataset, use the script "Dual_Driver.py" with appropriate parametes to train the inverse network.

Copyright 2020 Amanpreet Singh, Martin Bauer, Sarang Joshi

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

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• Amanpreet Singh (u1209323 at umail dot utah dot edu)
• Martin Bauer (bauer at math dot fsu dot edu)
• Sarang Joshi (sjoshi at sci dot utah dot edu)