Teaching Advanced numerical analysis I (EN)Construction and analysis of numerical methods for the solution of problems from linear algebra, integration, approximation, and differentiation. Set theory (EN)Set Theory as a foundational system for mathematics. ZF, ZFC and ZF with Atoms. Relative consistency of the Axiom of Choice, the Continuum Hypothesis, the reals as a countable union of countable sets, the existence of a countable family of pairs without any choice function, and so on.Scientific machine learning (EN)This course covers topics of scientific machine learning. Part I focuses on sequential-in-time training of nonlinear parametrizations for numerically solving partial differential equations. Part II treats generative modeling of physical processes. This is a project-based course.Intrusive and non-intrusive model reduction (EN)Intrusive and non-intrusive model reduction for parametrized partial differential equations and dynamical systems
