Physics-informed Neural Networks with Unknown Measurement Noise

Philipp Pilar, Niklas Wahlström
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:235-247, 2024.

Abstract

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-pilar24a, title = {Physics-informed neural networks with unknown measurement noise}, author = {Pilar, Philipp and Wahlstr\"{o}m, Niklas}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {235--247}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/pilar24a/pilar24a.pdf}, url = {https://proceedings.mlr.press/v242/pilar24a.html}, abstract = {Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.} }
Endnote
%0 Conference Paper %T Physics-informed Neural Networks with Unknown Measurement Noise %A Philipp Pilar %A Niklas Wahlström %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-pilar24a %I PMLR %P 235--247 %U https://proceedings.mlr.press/v242/pilar24a.html %V 242 %X Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.
APA
Pilar, P. & Wahlström, N.. (2024). Physics-informed Neural Networks with Unknown Measurement Noise. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:235-247 Available from https://proceedings.mlr.press/v242/pilar24a.html.

Related Material