Koopman early warning signals for bifurcation and rate-induced tipping

[2608.14716] Koopman early warning signals for bifurcation and rate-induced tipping Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences > Chaotic Dynamics arXiv:2608.14716 (nlin) [Submitted on 12 Aug 2026] Title: Koopman early warning signals for bifurcation and rate-induced tipping Authors: Juan Nathaniel , Carla Roesch , Derek DeSantis , Parvathi Kooloth , Hang Fan , Valerio Lucarini , Anastasia Romanou , Pierre Gentine View a PDF of the paper titled Koopman early warning signals for bifurcation and rate-induced tipping, by Juan Nathaniel and 7 other authors View PDF HTML (experimental) Abstract: Abrupt transitions in complex systems are often preceded by early warning signals. However, most indicators rely on the notion of critical slowing down and do not generally extend to rate-induced tipping where transitions can occur without local loss of stability. This is problematic in stochastic, nonautonomous systems where internal variability and time-varying variables interact to shape tipping onset. We use Koopman operator theory to develop a unified early warning framework for both bifurcation and rate-induced tipping in stochastic systems. Our approach builds on residual Koopman mode decomposition that measures discrepancies between dynamics and their finite-dimensional approximation, and extends it to the control setting by augmenting the observable space with time-varying control variables. In idealized examples, the resulting indicators recover expected signatures near bifurcation points and improve detection in rate-induced regimes where classical indicators fail. We further show that learned embeddings through deep learning outperform prescribed dictionaries, especially in a high-dimensional setting. Applied to simulations of the Atlantic Meridional Overturning Circulation, our Koopman-based indicators distinguish tipping from non-tipping trajectories and reveal interpretable spectral signatures prior to critical transition. Subjects: Chaotic Dynamics (nlin.CD) ; Machine Learning (cs.LG) Cite as: arXiv:2608.14716 [nlin.CD] (or arXiv:2608.14716v1 [nlin.CD] for this version) https://doi.org/10.48550/arXiv.2608.14716 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Juan Nathaniel [ view email ] [v1] Wed, 12 Aug 2026 01:33:22 UTC (13,673 KB) Full-text links: Access Paper: View a PDF of the paper titled Koopman early warning signals for bifurcation and rate-induced tipping, by Juan Nathaniel and 7 other authors View PDF HTML (experimental) TeX Source view license Current browse context: nlin.CD < prev | next > new | recent | 2026-08 Change to browse by: cs cs.LG nlin 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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