An Introductory Guide to Koopman Learning
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914114438168576 |
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| author | Colbrook, Matthew J. Drmač, Zlatko Horning, Andrew |
| author_facet | Colbrook, Matthew J. Drmač, Zlatko Horning, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Introductory Guide to Koopman Learning Colbrook, Matthew J. Drmač, Zlatko Horning, Andrew Numerical Analysis Machine Learning Dynamical Systems Optimization and Control Spectral Theory 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. |
| title | An Introductory Guide to Koopman Learning |
| topic | Numerical Analysis Machine Learning Dynamical Systems Optimization and Control Spectral Theory |
| url | https://arxiv.org/abs/2510.22002 |