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…
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…
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-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…