Some Experiences in Using Machine Learning Techniques for the Numerical Solution of Partial Differential Equations

Exploring the benefits and limitations of using techniques from machine learning (ML) for the numerical solution of partial differential equations (PDEs) is a current topic of research. This talk reports on a few experiences with such approaches for:- determining slope limiters for steady-state convection-diffusion problems, - computing the solution of steady-state convection-diffusion problems with physics-informed neural networks (PINNs),- trying to enhance the accuracy of time-dependent incompressible flow simulations on coarse grids with neural networks and fine grid data.