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 framework. In eDMD a compression of the lifted system dynamics on the space spanned by finitely many observables is computed, in which the original space is embedded as a low-dimensional manifold. While this manifold is invariant for the infinite-dimensional Koopman operator, this invariance is typically not preserved for its eDMD-based approximation. Hence, an additional (re-)projection step is often tacitly incorporated to improve the prediction capability. We propose a novel framework for consistent reprojectors respecting the underlying manifold structure. Further, we present a new geometric reprojector based on maximum-likelihood arguments, which significantly enhances the approximation accuracy and preserves known finite-data error bounds.
@article{arxiv.2307.16188,
title = {Reprojection methods for Koopman-based modelling and prediction},
author = {Pieter van Goor and Robert Mahony and Manuel Schaller and Karl Worthmann},
journal= {arXiv preprint arXiv:2307.16188},
year = {2023}
}