In practice, input data for mathematical models are never precisely known, but subject to various types of uncertainties. These can arise, for instance, from measurement errors or from limited available information. The subject of this lecture are methods for quantifying the resulting uncertainties in model outputs.
The course focuses on recent advances in approaches based on probabilistic models of uncertainty. An important class of applications are PDE models with uncertain coefficients, where one aims to extract information on the probability distributions of solutions. In a Bayesian framework, one can also treat corresponding inverse problems, where distributions of coefficients are reconstructed from noisy partial measurements of solutions. Besides Monte Carlo-type methods based on random sampling, one can also consider purely deterministic approximations of probability distributions, which leads to high-dimensional approximation problems.
Prerequisites: The course assumes basic knowledge on probability theory and on partial differential equations.
Mo 14 (c.t.) - 16 and Wed 8 - 10, Wegelerstr 6, SemR We 5.002