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.
@article{arxiv.2209.14115,
title = {Deep learning for gradient flows using the Brezis-Ekeland principle},
author = {Laura Carini and Max Jensen and Robert Nürnberg},
journal= {arXiv preprint arXiv:2209.14115},
year = {2023}
}
Comments
Proceeding of the Equadiff 15 conference (https://conference.math.muni.cz/equadiff15)