BOON: Boundary correction for neural operators

Nadim Saad*, Gaurav Gupta*, Shima Alizadeh, Danielle C. Maddix
Guiding continuous operator learning through Physics-based boundary constraints,
International Conference on Learning Representations, 2023
(*equal contribution authors)

Setup

Requirements

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.

Experiments

Data

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.

BOON PDE datasets

Scripts

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.

1D Heat equation motivating example

As an example, a complete pipeline is shown for the 1D single-step PDE with Neumann boundary condition in the attached examples_1d_single_step.ipynb notebook.

Non-physical solution: Nonzero flux suggests heat flow through an insulator.

1D Stokes' second problem

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.

2D Navier-Stokes lid-driven cavity flow

A complete pipeline is shown for the 2D time-varying PDE with Dirichlet boundary condition in the attached examples_3d_multi_step.ipynb notebook.

https://user-images.githubusercontent.com/19197210/217733438-211a4499-d2b3-4830-8bba-2d3d7ad5dfb3.mp4

https://user-images.githubusercontent.com/19197210/217733831-9d9336a3-6709-40f3-b326-716ab98a6d30.mp4

Citation

If you use this code, or our work, please cite:

@inproceedings{saad2022BOON,
  author = {Saad, Nadim and Gupta, Gaurav and Alizadeh, Shima and Maddix, Danielle C.},
  title = {Guiding continuous operator learning through Physics-based boundary constraints},
  booktitle={International Conference on Learning Representations},
  year={2023},
}