Nadim Saad*, Gaurav Gupta*, Shima Alizadeh, Danielle C. Maddix
Guiding continuous operator learning through Physics-based boundary constraints
arXiv:2212.07477
(*equal contribution authors)
The code package is developed using Python 3.8 and Pytorch 1.11 with cuda 11.6. The code could be executed on CPU/GPU but GPU is preferred. All experiments were conducted on Tesla V100 16GB.
Generate the data using the scripts provided in the 'Data' directory. The scripts use Matlab 2018+. A sample generated dataset for all the experiments is available below.
Detailed notebooks for reproducing all the experiments in the paper are provided. The cases of 1D, 1D time-varying, 2D time-varying are shown in the respective notebooks for all the three boundary conditions of Dirichlet, Neumann, and Periodic.
As an example, a complete pipeline is shown for the 1D time-varying PDE with Dirichlet boundary condition in the attached examples_1d_multi_step.ipynb
notebook.
A complete pipeline is shown for the 2D time-varying PDE with Dirichlet boundary condition in the attached examples_3d_multi_step.ipynb
notebook.
If you use this code, or our work, please cite:
@misc{saad2022BOON,
author = {Saad, Nadim and Gupta, Gaurav and Alizadeh, Shima and Maddix, Danielle C.},
title = {Guiding continuous operator learning through Physics-based boundary constraints},
publisher = {arXiv},
year = {2022},
doi = {10.48550/ARXIV.2212.07477},
}