QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression

JCP | arXiv

Kevin Doherty*, Cooper Simpson*, Stephen Becker, Alireza Doostan

Published in Journal of Computational Physics

Abstract

We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. Moreover, the construction of our operator admits an efficient implementation which we detail and construct. In the setting of compressing data arising from partial differential equation (PDE) simulations, we show that QuadConv can match the performance of standard discrete convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to a standard convolutional autoencoder (CAE). Further, we show that the QCAE can maintain this accuracy even on non-uniform data.

License & Citation

All source code is made available under an MIT license. You can freely use and modify the code, without warranty, so long as you provide attribution to the authors. See LICENSE for the full text.

Our paper can be cited using the following bibtex entry:

@article{quadconv,
	title = {{QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression}},
	author = {Doherty, Kevin and Simpson, Cooper and Becker, Stephen and Doostan, Alireza},
	year = {2023},
	journal = {J. Comp. Physics, {\em to appear}},
	doi = {10.1016/j.jcp.2023.112636}
}

Usage

Note that the QuadConv software has moved to PyTorch-QuadConv. This repository is still independently operational in order to maintain reproducibility of our results.

Repository Structure

• core: Model architectures, data loading, core operators, and utilities.
• data: Data folders
• experiments: Experiment configuration files
  • template.yaml: Detailed experiment template
• job_scripts: HPC job submission scripts
• lightning_logs: Experiment logs
• notebooks: Various Jupyter Notebooks for recreating paper figures
• main.py: Model training and testing script

Environment Setup

The file environment.yaml contains a list of dependencies, and it can be used to generate an anaconda environment with the following command:

conda create --file=environment.yaml

which will install all necessary packages in the conda environment QuadConv. It might be faster in some cases to just install the packages individually. We would recommend installing the PyTorch, Nvidia, and PYG packages together, followed by the default packages, and then the pip packages.

For local development, it is easiest to install core as a pip package in editable mode using the following command from within the top level of this repository:

pip install -e .

The main experiment script can still be run without doing this, but the notebooks will be non-functional.

Data Acquisition

Our datasets are included in this repository using Git LFS.

Running Experiments

Use the following command to run an experiment:

python main.py --experiment <path/to/YAML/file/in/experiments>

If logger is set to True in the YAML config file, then the results of this experiment will be saved to lightning_logs/<path/to/YAML/file/in/experiments>.

To visualize the logging results saved to lightning_logs/ using tensorboard run the following command:

tensorboard --logdir=lightning_logs/