In recent years, much attention and research has been devoted to the Koopman operator following the seminal 2005 work [1] by Mesic. The Koopman operator offers the possibility to exactly transform any dynamical system described by a (sufficiently smooth) autonomous nonlinear differential equation for its states into a (generally infinite-dimensional) decoupled linear system. More precisely, the Koopman operator is a (semi)group of linear operators with a generator that describes the so-called Kolmogorov forward equation. The time dependence of any eigenfunction φ of the Koopman operator (and its generator) is given by dφ/dt = λφ, where λ is the corresponding eigenvalue.

Much of the current research focuses on data-driven methods for system modeling and identification, spurred by the development of dynamic mode decomposition [2] and its extensions [3] in the fluid dynamics community. These methods are algorithms for estimating eigenvalues and eigenfunctions of the Koopman operator from time series data. The core idea is a least-squares regression of ansatz functions (often referred to as a library) to map many initial states x(0) to their corresponding states x(T) after the same time interval T, resulting from the flow of the dynamical system. ... mehr

Much of the current research focuses on data-driven methods for system modeling and identification, spurred by the development of dynamic mode decomposition [2] and its extensions [3] in the fluid dynamics community. These methods are algorithms for estimating eigenvalues and eigenfunctions of the Koopman operator from time series data. The core idea is a least-squares regression of ansatz functions (often referred to as a library) to map many initial states x(0) to their corresponding states x(T) after the same time interval T, resulting from the flow of the dynamical system. ... mehr

Zugehörige Institution(en) am KIT |
Institut für Technische Mechanik (ITM) |

Publikationstyp |
Vortrag |

Publikationsdatum |
30.05.2023 |

Sprache |
Englisch |

Identifikator |
KITopen-ID: 1000162282 |

Veranstaltung |
93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2023), Dresden, Deutschland, 30.05.2023 – 02.06.2023 |

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