Hybrid Methods for Poisson and Stokes

Abstract

In this talk two different hybrid approaches which both combine physical knowledge with neural networks are examined. First, we consider physics-informed neural networks which embed the differential equations into the loss function of a neural network. Second, we present our novel hybrid approach which incorporates the residual of the finite element formulation on a discretization into the loss function of a neural network. Both methods are trained without data from simulations or measurements, but rely on the partial differential equation itself. Finally, we evaluate the methods applied to the Poisson equation and the Stokes flow.