Deterministic and Stochastic Modeling and Simulation

Lecture: Prof. Dr.-Ing. Ulrich Römer

This course covers advanced topics in the parametric simulation of technical and physical systems governed by differential equations. Parametric modeling and simulation are studied from both deterministic and stochastic perspectives. While the course is motivated by practical examples, its primary objective is to develop and deepen the understanding of the underlying mathematical concepts. The course builds on prior knowledge of finite element modeling and uncertainty quantification.

Core topics include:

• Strong and weak formulation of the Poisson and Helmholtz equation
• Galerkin finite element method
• Parametric modeling techniques
• Reduced-order modeling
• Gaussian process regression
• Sparse grid methods
• Bayesian modeling