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Keywords:
machine learning; deep neural networks; gradient flows; Brezis–Ekeland principle; adversarial networks; differential equations
machine learning; deep neural networks; gradient flows; Brezis–Ekeland principle; adversarial networks; differential equations
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, 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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