### V5E5 Advanced Topics in Numerical Analysis

## Numerical Methods in Uncertainty Quantification

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:*

- Probability measures on Banach spaces
- Monte Carlo and related methods
- Spectral approximations
- Uncertainty propagation in PDE models
- The Bayesian approach to inverse problems

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

#### When & where:

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

#### Final Exam

Oral exam, by individual appointment.