7 papers · 1 filter
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-based predictions and bifurcation analysis of parametric dynamical systems
Pieter van Goor, Robert Mahony, Manuel Schaller +1
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of t…
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…
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 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…