Applied Mathematical Seminar35: Adaptive solution for PDEs and generative models

Seminar| Institute of Mathematical Sciences

Abstract: Numerically solving PDEs generally requires mesh generation in order to compute the discrete numerical solution. Adaptive mesh refinement is necessary if the true solution has low regularity. We introduce a new class of robust a posterioriori estimation techniques for the adaptive solution of elliptic problems with high-contrast coefficients. We demonstrate the performance with numerical examples. In the second part of the talk, we discuss generative models in artificial intelligence and introduce a new normalizing flow model called AUTM.