Lap2Dpinn

Introduction

The Lap2Dpinn tool estimates a solution of 2D Laplace PDE with abitrary boundary conditions defined on a 128x128 8-bit image domain using a pre-trained multi-class segmentation U-net model.

Key Features

The Lap2Dpinn tool is called from command line as follows:

Lap2Dpinn input_folder output_folder model_file,

where input_folder is the path to the folder with input 128x128 images stored as *.png, output_folder is the folder where output images (i.e. solutions of forward or inverse 2D Laplace boundary value problems) are saved, and the model_file is either forward or inverse h5 model. Forward Lap2Dpinn takes sparse images (such as examples in the folder 'input') where boundary conditions are defined by non-zero (i.e. non-black) values and writes out 2D Laplace smoothed (non-sparse) images (such as examples in the folder 'output'). Example of the command line call for the forward solution is below:

.\Lap2Dpinn.exe input output data128_70k_forward.h5

Inverse Lap2Dpinn takes smoothed (non-sparse) images (such as examples in the folder 'output') and computes sparse images resembing the boundary conditions of the corresponding 2D Laplace BVP (such as examples in the folder 'input'). Example of the command line call for the inverse solution is below:

.\Lap2Dpinn.exe output input data128_70k_inverse.h5

In general, arbitrary grayscale 8-bit images can be used as input for forward and inverse Lap2Dpinn computations. However, meaningful input images for the forward 2D Laplace PINN are sparse images such as examples in the folder 'input', and smoothed images such as example in the 'output' folder for the inverse 2D Laplace PINN.

Downloads

The Lap2Dpinn tool for Linux and Windows OS with example data can be downloaded using the links below:

Download the Lap2Dpinn tool for Windows x64 (500MB)
Download the Lap2Dpinn tool for Linux (500MB)

By downloading, installing and/or using this software the user agrees with the following license conditions.

This software requires MATLAB R2021a run-time libraries to be installed:

Download MATLAB R2021a run-time for Windows x64 (~2GB).
Download MATLAB R2021a run-time for Linux (~2GB).

Windows users should also install the run-time components from the following link: https://www.microsoft.com/en-us/download/details.aspx?id=48145.

References

[1] Antony et al. (2022) Deep learning multi-class segmentation as a PINN solver: a feasibility study of the 2D Laplace PDE.

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