2022-06-28-brandstetter22a.md

title	booktitle	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Lie Point Symmetry Data Augmentation for Neural PDE Solvers	Proceedings of the 39th International Conference on Machine Learning	Neural networks are increasingly being used to solve partial differential equations (PDEs), replacing slower numerical solvers. However, a critical issue is that neural PDE solvers require high-quality ground truth data, which usually must come from the very solvers they are designed to replace. Thus, we are presented with a proverbial chicken-and-egg problem. In this paper, we present a method, which can partially alleviate this problem, by improving neural PDE solver sample complexity—Lie point symmetry data augmentation (LPSDA). In the context of PDEs, it turns out we are able to quantitatively derive an exhaustive list of data transformations, based on the Lie point symmetry group of the PDEs in question, something not possible in other application areas. We present this framework and demonstrate how it can easily be deployed to improve neural PDE solver sample complexity by an order of magnitude.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	brandstetter22a	0	Lie Point Symmetry Data Augmentation for Neural {PDE} Solvers	2241	2256	2241-2256	2241	false	Brandstetter, Johannes and Welling, Max and Worrall, Daniel E	given family Johannes Brandstetter given family Max Welling given family Daniel E Worrall	2022-06-28		Proceedings of the 39th International Conference on Machine Learning	162	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v162/brandstetter22a/brandstetter22a.pdf