274 citations · 1.8k across the 48 of their papers we have counts for
6 papers · 1 filter
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…
Continuous Relaxations for the Traveling Salesman Problem
Tuhin Sahai, Adrian Ziessler, Stefan Klus +1
In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the t…