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.