Research Group of Prof. Dr. M. Bachmayr
Institute for Numerical Simulation

V5E5   Advanced Topics in Numerical Analysis

Numerical Methods in Uncertainty Quantification

Prof. Dr. Markus Bachmayr

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.

Planned contents:

Prerequisites: The course assumes basic knowledge on probability theory and on partial differential equations.

Final Exam

Oral exam, by individual appointment.

Please choose from the following dates: February 5, 6, 26, 27. (Dates for a second attempt will be offered in the last week of March, i.e. 26th to 30th)

Subject matter of the exam: chapters 1, 2, and 3 of the lecture notes (i.e., chapter 4 is excluded)

Supporting materials

Coding examples in Julia: (To run the code in these notebooks yourself, you can either log in to JuliaBox and use them remotely after uploading them there, or install Julia and IJulia on your own machine by first downloading Julia from here and following the installation instructions here and here.)

When & where:

Mo 14 (c.t.) - 16 and Wed 8 - 10, Wegelerstr 6, SemR We 5.002


For further literature, see also the lecture notes. In each category below, the items that are most relevant for the course come first: