{"ID":2850842,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22002","arxiv_id":"2510.22002","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2510.22002","url_pdf":"https://arxiv.org/pdf/2510.22002v1","authors":"[\"Matthew J. Colbrook\",\"Zlatko Drmač\",\"Andrew Horning\"]","published":"2025-10-24T20:09:22Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\",\"math.DS\",\"math.OC\",\"math.SP\"]","methods":"[]","has_code":false}