274 citations · 1.8k across the 48 of their papers we have counts for
5 papers · 2 filters
Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
Stefan Klus, Ingmar Schuster, Krikamol Muandet
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operato…
Diffusion maps tailored to arbitrary non-degenerate Ito processes
Ralf Banisch, Zofia Trstanova, Andreas Bittracher +2
We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling de…
Koopman operator-based model reduction for switched-system control of PDEs
Sebastian Peitz, Stefan Klus
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimens…
Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics
Andreas Bittracher, Péter Koltai, Stefan Klus +3
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhi…
Data-driven model reduction and transfer operator approximation
Stefan Klus, Feliks Nüske, Péter Koltai +4
In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to ap…