2024-06-30-doumeche24a.md

title	section	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
Physics-informed machine learning as a kernel method	Original Papers	Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. We prove that for linear differential priors, the problem can be formulated as a kernel regression task. Taking advantage of kernel theory, we derive convergence rates for the minimizer $\hat f_n$ of the regularized risk and show that $\hat f_n$ converges at least at the Sobolev minimax rate. However, faster rates can be achieved, depending on the physical error. This principle is illustrated with a one-dimensional example, supporting the claim that regularizing the empirical risk with physical information can be beneficial to the statistical performance of estimators.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	doumeche24a	0	Physics-informed machine learning as a kernel method	1399	1450	1399-1450	1399	false	Doum{\`e}che, Nathan and Bach, Francis and Biau, G{\'e}rard and Boyer, Claire	given family Nathan Doumèche given family Francis Bach given family Gérard Biau given family Claire Boyer	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/doumeche24a/doumeche24a.pdf