High-Dimensional Partial Differential Equations

What it is about

You learn how partial differential equations appear in very high dimensions, what theoretical peculiarities and numerical difficulties (e.g., Curse of Dimensionality) arise, and which modern solution approaches exist. In the end you will be able to analyze theoretical properties of solutions and implement and apply various numerical methods (sparse grids, tensor decompositions, neural networks) to applications.

What you will be able to do

• Understanding the special challenges of high-dimensional PDEs
• Analysis of theoretical properties of solutions in high dimensions
• Implementation and comparison of modern numerical methods for high-dimensional problems
• Application of the methods to relevant case studies in science and engineering

What the module consists of

• VorlesungConveying theoretical concepts, derivations and solution strategies
• Tutorium/ÜbungsgruppeDeepening through collaborative discussions, exercises and presentation of solutions

Teaching method

• Interaktive VorlesungenExplanation of theoretical foundations, derivations and joint problem solving
• Tutorien/ProblemklassenStrengthening analytical and computational skills through exercises and exchange