Deep learning for gradient flows using the Brezis-Ekeland principle

• URL: http://arxiv.org/abs/2209.14115v1
• Date: Wed, 28 Sep 2022 14:06:32 GMT
• Title: Deep learning for gradient flows using the Brezis-Ekeland principle
• Authors: Laura Carini, Max Jensen, Robert N\"urnberg
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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