Numerical Analysis and Scientific Computing Seminar | Emmanuel Franck, Enhanced Discontinuous Galerkin schemes by neural networks

Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link) 

Speaker

Emmanuel Franck, Researcher INRIA

Title

Enhanced Discontinuous Galerkin schemes by neural networks

Abstract

In this work, we propose to introduce two methods for enriching DG diagrams using learning techniques. The introduction will explain the links between scientific computing and learning methods, and the contribution that the latter can make. Two examples in a discontinuous Galerkin framework for hyperbolic equations will then be introduced. First, we will show how we can improve the accuracy of schemes using parametric physic informed neural networks. The link between these methods and classical numerical methods will also be illustrated. Secondly, we will propose a learning approach close to optimal control methods for constructing new artificial viscosities for these schemes.  Both examples will be illustrated with numerical results. In conclusion, the possibilities of hybridation between machine learning and DG methods will be discussed more generally.