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.
Referent: Prof. Dr. Robert Scheichl, Universität Heidelberg
Zeit: 17:15 - 18:30 Uhr
Ort: Gebäude 48, Raum 210
Die Vorträge des Felix-Klein-Kolloquiums finden jeweils um 17.15 Uhr im Raum 210 des Mathematik-Gebäudes 48 statt. Zuvor gibt es ab 16.45 Uhr die Gelegenheit, die Sprecherin oder den Sprecher beim Kolloquiumstee in Raum 580 zu treffen.