An Introductory Guide to Koopman Learning

Matthew J. Colbrook; Zlatko Drmač; Andrew Horning

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arXiv · 2510.22002

An Introductory Guide to Koopman Learning

Matthew J. Colbrook·Zlatko Drmač·Andrew Horning

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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.

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Matthew J. Colbrook, Zlatko Drmač, Andrew Horning. 2025-10-24. An Introductory Guide to Koopman Learning. https://arxiv.org/abs/2510.22002

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