An Introductory Guide to Koopman Learning
Abstract
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman learning, emphasizing rigorously convergent data-driven methods for forecasting and spectral analysis. We provide a unified account of error control via residuals in both finite- and infinite-dimensional settings, an elementary proof of convergence for generalized Laplace analysis -- a variant of filtered power iteration that works for operators with continuous spectra and no spectral gaps -- and review state-of-the-art approaches for computing continuous spectra and spectral measures. The goal is to provide both newcomers and experts with a clear, structured overview of reliable data-driven techniques for Koopman spectral analysis.
Cite
@article{arxiv.2510.22002,
title = {An Introductory Guide to Koopman Learning},
author = {Matthew J. Colbrook and Zlatko Drmač and Andrew Horning},
journal= {arXiv preprint arXiv:2510.22002},
year = {2025}
}