T1: Data-driven Dynamical Systems

Format

Compact course

Description

Natural processes often follow an evolution law given by a (nonlinear) dynamical system. In some cases, quite explicit mathematical formulas for the dynamical system are known, e.g., for the motion of a marble on a flat surface without friction, perturbation or any kind of noise. However, in more advanced applications and more natural settings, the natural process can only be observed and described by a discrete set of measured data. With classical methodologies, the parameters describing the dynamical system typically cannot be identified from the measured data or, if the situation is sufficiently well-behaved, parameter identification is possible only with an enormous amount of effort and often only up to some uncertainty. In recent years, a new methodology arose to investigate data-driven dynamical systems: Koopman operator theory, Koopman spectral analysis or more general transfer operator based techniques. This compact course will provide an introduction to this topic.