Deep learning for gradient flows using the Brezis-Ekeland principle

Autor:	Laura Carini, Max Jensen, Robert Nürnberg
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	FOS: Computer and information sciences Computer Science - Machine Learning General Mathematics 35K15 35A15 68T07 FOS: Mathematics Numerical Analysis (math.NA) Mathematics - Numerical Analysis Machine Learning (cs.LG)
Popis:	We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis--Ekeland principle, which naturally defines an objective function to be minimized, and so is ideally suited for a machine learning approach using deep neural networks. We describe our approach in a general framework and illustrate the method with the help of an example implementation for the heat equation in space dimensions two to seven. Proceeding of the Equadiff 15 conference (https://conference.math.muni.cz/equadiff15)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::156df5b50a7357db7c4d1c478879a2a7 http://arxiv.org/abs/2209.14115 Zobrazit plný text záznamu