Appears in collection : Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration

I will give an elementary introduction of basic deep learning models and training algorithms from a mathematical viewpoint. In particular, I will relate some basic deep learning models with finite element and multigrid methods. I will also touch on some advanced topics to demonstrate the potential of new mathematical insight and analysis for improving the efficiency of deep learning technologies and, in particular, for their application to numerical solution of partial differential equations.