Deep learning for gradient flows using the Brezis-Ekeland principle

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.

Proceeding of the Equadiff 15 conference (https://conference.math.muni.cz/equadiff15)

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