PICR :: Physics-Informed Convolutional Neural Networks for Corruption Removal on Dynamical System

Authors: Daniel Kelshaw, Luca Magri
Venue: Accepted to NeurIPS 2022 Workshop on Machine Learning and the Physical Sciences

Abstract

Measurements on dynamical systems, experimental or otherwise, are often subjected to inaccuracies capable of introducing corruption; removal of which is a problem of fundamental importance in the physical sciences. In this work we propose physics-informed convolutional neural networks for stationary corruption removal, providing the means to extract physical solutions from data, given access to partial ground-truth observations at collocation points. We showcase the methodology for 2D incompressible Navier-Stokes equations in the chaotic-turbulent flow regime, demonstrating robustness to modality and magnitude of corruption.

 

 

Getting Started

All code to reproduce experiments can be found in the ./src folder:

1. Generate data using ./src/data/generate_*.py
2. Run Experiments using ./src/experiments/mp_*_experiment.py
3. Run post-processing using ./src/postprocessing/produce_paper_results.ipynb

Defaults have been set to the same as used in the paper.

Note: the post-processing relies on a particular file structure:

<experiment_folder>/<MAG/FREQ>/<system_name>/<experiment_id>/<repeat>

The ./src/experiments/mp_*_experiment.py handles the final two fields.

Citation

@inproceedings{Kelshaw2022,
  title = {Physics-Informed Convolutional Neural Networks for Corruption Removal on Dynamical Systems},
  author = {Daniel Kelshaw and Luca Magri},
  booktitle = {NeurIPS 2022 Workshop on Machine Learning and the Physical Sciences},
  year = {2022},
  url = {https://arxiv.org/abs/2210.16215}
}