Advanced Numerical Methods - Model Reduction of Dynamical Systems

This course is an introduction to model reduction techniques for linear and nonlinear dynamical systems.

Numerical models relevant for applied and science and engineering often deal with increasingly intricate physical processes, leading to complex governing equations that are often high-dimensional or only partially understood. Furthermore, most of these phenomena are dynamic and intrinsically nonlinear, which makes computational predictions challenging, if not entirely infeasible.

In this course, a student will learn the essential techniques to obtain rigorous reduced-order models (ROM) for very high-dimensional dynamical systems. We will techniques that obtain these ROMs directly from governing equations as well as data-driven techniques, that do not require knowledge of the governing equations (see learning objectives for an overview).

In addition to classical techniques that are provably effective for reducing linear systems, we will discuss modern techniques that enable robust model reduction for nonlinear systems along with relevant computational tools. Students will get to work examples of dynamical systems from diverse application fields, including mechanical systems, fluid flows, MEMS models, among others.