Solving the Dirichlet problem for the Monge-Ampère equation

Abstract: The Monge-Ampère equation is a fully nonlinear PDE of fundamental importance in analysis, geometry and in the applied sciences. We present two methods for numerically solving the Dirichlet problem for the Monge-Ampère equation using deep neural networks. In the numerical examples we study the effect of singularities, discontinuities and noise in the source function, and investigate the performance in higher dimensions as well as on nontrivial domains.

Contact Antti Perälä to receive the Zoom link.