An Introductory Guide to Koopman Learning

Matthew Colbrook (), Zlatko Drmač () and Andrew Horning ()
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Matthew Colbrook: University of Cambridge, Department of Applied Mathematics and Theoretical Physics
Zlatko Drmač: University of Zagreb, Department of Mathematics
Andrew Horning: Rensselaer Polytechnic Institute, Department of Mathematical Sciences

Chapter 106 in Operator Theory, 2026, pp 3247-3295 from Springer

Abstract: 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 chapter, 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.

Keywords: Data-driven dynamics; Koopman operator; Dynamic Mode Decomposition; Generalized Laplace analysis; Spectral measures (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_126

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