论文标题
使用布雷兹斯 - 欧洲原则进行梯度流的深度学习
Deep learning for gradient flows using the Brezis-Ekeland principle
论文作者
论文摘要
我们提出了一种深度学习方法，用于作为梯度流的偏微分方程的数值解。该方法依赖于Brezis - ekeland原理，该原则自然定义了要最小化的目标函数，因此理想地适合使用深神经网络的机器学习方法。我们在一般框架中描述了我们的方法，并借助于二到七个空间维度的热量方程的示例实现来说明方法。
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.
