Numerical methods for parametric and random differential equations in SoSe 2025

Prof. Dr. Markus Bachmayr
Hannah Behrens ✉

Dates

Contents

• Parameter-dependent partial differential equations and parametric regularity
• Problems with random coefficients as parametric problems
• Basic theory of random fields and random function series
• Sparse polynomial approximations in finite and infinite dimensions
• Low-rank approximations and model reduction
• Neural network-based approximations
• Sparse interpolation (stochastic collocation)
• Stochastic Galerkin discretizations and iterative methods for sparse and low-rank approximations
• Discrete least squares methods

The accompanying tutorials comprise both exercises on the theory and the implementation of numerical methods using the Julia programming language (no previous knowledge of Julia is required).

Prerequisites

Basic knowledge on the discretization of boundary value problems (as treated in Numerical Analysis III) is required, Numerical Analysis IV is helpful. The default language of the course will be English.

Moodle

Further information, literature and materials are provided in Moodle.