45 citations · 147 across the 71 of their papers we have counts for
13 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…
On Data-Driven Unbiased Predictors using the Koopman Operator
Roland Schurig, Pieter van Goor, Karl Worthmann +1
The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dyn…
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…
Shaping the Koopman dictionary by learning on the Grassmannian
Roland Schurig, Pieter van Goor, Karl Worthmann +1
Extended dynamic mode decomposition (EDMD) is a powerful tool to construct linear predictors of nonlinear dynamical systems by approximating the action of the Koopman operator on a…
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…