# A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

31 Mar 2019Gitta KutyniokPhilipp PetersenMones RaslanReinhold Schneider

We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low-dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical neural network approximation results... (read more)

PDF Abstract