Nonparametric Sparse Online Learning of the Koopman Operator

[2405.07432] Nonparametric Sparse Online Learning of the Koopman Operator Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2405.07432 (stat) [Submitted on 13 May 2024 ( v1 ), last revised 15 Apr 2026 (this version, v4)] Title: Nonparametric Sparse Online Learning of the Koopman Operator Authors: Boya Hou , Sina Sanjari , Nathan Dahlin , Alec Koppel , Subhonmesh Bose View a PDF of the paper titled Nonparametric Sparse Online Learning of the Koopman Operator, by Boya Hou and 4 other authors View PDF HTML (experimental) Abstract: The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present a sparse online learning algorithm that learns the Koopman operator iteratively via stochastic approximation, with explicit control over model complexity and provable convergence guarantees. Specifically, we study the Koopman operator via its action on the reproducing kernel Hilbert space (RKHS), and address the mis-specified scenario where the dynamics may escape the chosen RKHS. In this mis-specified setting, we relate the Koopman operator to the conditional mean embeddings (CME) operator. We further establish both asymptotic and finite-time convergence guarantees for our learning algorithm in mis-specified setting, with trajectory-based sampling where the data arrive sequentially over time. Numerical experiments demonstrate the algorithm's capability to learn unknown nonlinear dynamics. Comments: 44 pages Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Systems and Control (eess.SY) MSC classes: 46E22, 47B32, 93B40, 93E12, 93E35 Cite as: arXiv:2405.07432 [stat.ML] (or arXiv:2405.07432v4 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2405.07432 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Boya Hou [ view email ] [v1] Mon, 13 May 2024 02:18:49 UTC (223 KB) [v2] Tue, 4 Feb 2025 20:17:37 UTC (2,373 KB) [v3] Tue, 29 Jul 2025 02:34:46 UTC (1,199 KB) [v4] Wed, 15 Apr 2026 00:30:16 UTC (884 KB) Full-text links: Access Paper: View a PDF of the paper titled Nonparametric Sparse Online Learning of the Koopman Operator, by Boya Hou and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2024-05 Change to browse by: cs cs.LG cs.SY eess eess.SY stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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