45 citations · 144 across the 50 of their papers we have counts for
11 papers · 1 filter
Extended dynamic mode decomposition with Fourier dictionaries: Error bounds and fast implementation
Felix Bartel, Sandra Ritter, Manuel Schaller +1
The Koopman operator has gained considerable attention in dynamical systems due to its capability to provide a linear viewpoint for nonlinear systems using data-driven methods such…
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Maximiliano Hertel, Ilja Klebanov, Manuel Schaller +1
Conditional expectation operators (CEOs) and their associated conditional mean embeddings (CMEs) play a central role across applied mathematics and machine learning, appearing in n…
Koopman for stochastic dynamics: error bounds for kernel extended dynamic mode decomposition
Maximiliano Hertel, Friedrich M. Philipp, Manuel Schaller +1
We prove -error bounds for kernel extended dynamic mode decomposition (kEDMD) approximants of the Koopman operator for stochastic dynamical systems. To this end, we estab…
Maximum-likelihood reprojections for reliable Koopman predictors of parametric nonlinear dynamical systems
Pieter van Goor, Robert Mahony, Manuel Schaller +1
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, system analysis, learning, and prediction are considered through the lens o…
Group-Convolutional Extended Dynamic Mode Decomposition
Hans Harder, Feliks Nüske, Friedrich M. Philipp +3
This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolu…
-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition
Frederik Köhne, Friedrich M. Philipp, Manuel Schaller +2
Extended dynamic mode decomposition (EDMD) is a well-established method to generate a data-driven approximation of the Koopman operator for analysis and prediction of nonlinear dyn…
Variance representations and convergence rates for data-driven approximations of Koopman operators
Friedrich M. Philipp, Manuel Schaller, Septimus Boshoff +3
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; b…
Error analysis of kernel EDMD for prediction and control in the Koopman framework
Friedrich Philipp, Manuel Schaller, Karl Worthmann +2
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is…
Reprojection methods for Koopman-based modelling and prediction
Pieter van Goor, Robert Mahony, Manuel Schaller +1
Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman…
Equivariance and partial observations in Koopman operator theory for partial differential equations
Sebastian Peitz, Hans Harder, Feliks Nüske +3
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying line…
Error bounds for kernel-based approximations of the Koopman operator
Friedrich Philipp, Manuel Schaller, Karl Worthmann +2
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation…