High- or infinite-dimensional inverse problems in the context of complex physical systems arise in many science and engineering applications, such as in parameter identification or data assimilation problems. Sampling-based Bayesian inference provides an approach that allows in principle to solve this problem and to provide a quantification of uncertainties without suffering from the curse of dimensionality. In contrast to the very popular deep neural network approaches in machine learning, it comes with a theoretical framework that allows in many cases to rigorously analyse their performance and complexity. However, to bring these sampling methods in the feasible range for practical problems it is in general necessary to improve classical approaches, such as random-walk Metropolis-Hastings MCMC.
The lecture focuses on ways to directly accelerate classical Monte Carlo based inference approaches via multilevel or quasi-Monte Carlo ideas, as well as variational inference approaches that aim at finding a tractable transport map from a reference measure to the target measure for an efficient treatment of high dimensional Bayesian inverse problems.
Speaker: Prof. Dr. Robert Scheichl, University of Heidelberg
Time: 17:15 - 18:30 o'clock
Place: Building 48, room 210
The lectures of the Felix Klein Colloquium will be held at 17:15 in room 210 of the Mathematics Building 48. Beforehand - from 16:45 - there will be an opportunity to meet the speaker at the colloquium tea in room 580.