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Deep learning for gradient flows using the Brezis–Ekeland principle

Carini, Laura; Jensen, Max; Nürnberg, Robert; (2023) Deep learning for gradient flows using the Brezis–Ekeland principle. Archivum Mathematicum , 59 (3) pp. 249-261. 10.5817/am2023-3-249. Green open access

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Abstract

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.

Type: Article
Title: Deep learning for gradient flows using the Brezis–Ekeland principle
Open access status: An open access version is available from UCL Discovery
DOI: 10.5817/am2023-3-249
Publisher version: http://dx.doi.org/10.5817/AM2023-3-249
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Machine learning; deep neural networks; gradient flows; Brezis–Ekeland principle; adversarial networks; differential equations
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10165976
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