A special issue of European Journal of Applied Mathematics

The last few years have seen a resurgence of interest in artificial neural networks driven mainly by increasing computational resources and the availability of immense data sets. Aside from their use in main stream data science applications, deep networks (i.e., neural networks with many hidden layers) have led to new techniques for solving partial differential equations, particularly in high-dimensional settings. At the same time, the interpretation of some deep neural networks as nonlinear (partial) differential equations has led to a new frontier to gain theoretical insight and design new algorithms for deep learning. Motivated by these trends, this special issue brings together new results at this new interface between applied mathematics and data science.  

Topics:

• deep learning for solving high-dimensional PDEs
• deep learning for real-time PDE solution
• deep learning for reduced order modeling
• discovery of PDEs through deep learning
• uncertainty quantification of PDEs with deep learning
• new theory for deep learning using PDE techniques
• relations between deep learning, optimal control and mean-field games

Deadline for Submissions: September 30, 2019

Guest Editors:

Martin Burger, Friedrich-Alexander Universität Erlangen-Nürnberg, martin.burger@fau.de

Weinan E, Princeton University, weinan@math.princeton.edu

Lars Ruthotto, Emory University, lruthotto@emory.edu

Stanley Osher, UCLA, sjo@math.ucla.edu