High-Dimensional Approximation and Sampling in Uncertainty Quantification

Abstract: Uncertainty quantification plays an important role in many engineering applications. In this talk we discuss some recent advancements in the approximation of high- dimensional functions appearing in this context. We provide new results for surrogate modeling and parameter estimation in cases where the uncertainty is described by a Gaussian random field. Additionally we address how the usage of neural networks to learn linear and nonlinear operators may help in solving such tasks, and what possible challenges might lie ahead.

Venue: Mathematikon • Conference Room 5/104 / 5th Floor • Im Neuenheimer Feld 205 • 69120 Heidelberg