[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126864-en":3,"doc-seo-126864-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},126864,1099523885336,"Violet","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation - Abstract and introduction","Anticipating a tipping point—an abrupt transition between stable steady states—is difficult for nonautonomous dynamical systems, especially when the system dynamics near tipping lack deterministic oscillations. A reservoir-computing, data-driven machine-learning framework leverages noise to detect early warning patterns and predict potential future tipping. The approach is validated across examples from multiple fields. As an application, it estimates a possible collapse window for the Atlantic Meridional Overturning Circulation (AMOC) influenced by climate-driven freshwater changes, aligning with existing literature trends.","arXiv:2402.14877v2 [[physics. ao-ph](physics. ao-ph)] 17 Oct 2024  \nMachine-learning prediction of tipping with applications to the Atlantic Meridional  \nOverturning Circulation  \nShirin Panahi, 1 Ling-Wei Kong, 1 Mohammadamin Moradi, 1 Zheng-Meng  \nZhai, 1 Bryan Glaz,2 Mulugeta Haile,3 and Ying-Cheng Lai 1, 4, ∗  \n1 School of Electrical, Computer, and Energy Engineering,  \nArizona State University, Tempe, AZ 85287, USA  \n2 Army Research Directorate, DEVCOM Army Research Laboratory,  \n2800 Powder Mill Road, Adelphi, MD 20783-1138, USA  \n3 Army Research Directorate, DEVCOM Army Research Laboratory,  \n6340 Rodman Road, Aberdeen Proving Ground, MD 21005-5069, USA  \n4 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA  \n(Dated: October 18, 2024)  \nAnticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climateinduced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.  \nINTRODUCTION  \nA tipping point in nonlinear and complex dynamical systems is referred to as a transition from one stable steady state supporting the normal functioning of the system to another that can often be catastrophic and corresponds to system collapse [1] . This can happen asa system parameter passes through a critical point. For example, in ecosystems, before tipping the system is in a survival state with healthy species populations, while the state after the tipping is associated with extinction [1– 8] . In the past decade, tipping point in ecosystems has been extensively studied [1–4, 6–26] . The phenomenon of tipping can also arise in other contexts such as epidemic outbreak [27], a sudden transition from normal to depressed mood in bipolar patients [28], alterations in the stability of the Amazon rain forest [29], an increase in the carbon emission from Boreal permafrost [30], and the melting of Arctic sea ice [31] . A likely scenario by which a tipping point can occur is when a parameter of the system varies with time-nonautonomous dynamical systems. Suppose the system is in a normal functioning state at the present. Due to the parameter change, at a certain time in the future a critical point will be crossed, leading to a catastrophic tipping. The global climate change is causing ecosystems and climate systems of different scales to become such nonautonomous dynamical systems with the increasing risk of tipping. Articulating effective methods to reliably anticipate tipping is an urgent problem with broad implications and applications.  \n∗ [Ying-Cheng.Lai@asu.edu](Ying-Cheng.Lai@asu.edu)  \nIn this paper, we develop a reservoir-computing framework tailored to anticipating tipping in nonautonomous dynamical systems and demonstrate its predictive power using examples from different fields. A particular application that provided the main motivation for our work is predicting the possible collapse of the Atlantic Meridional Overturning Circulation (AMOC) [32–34] that supports moderate and livable temperature conditions in Western Europe [35] . The AMOC transports warmer, upper waters in the Atlantic northward and returns colder, deeper wat","cbCailHws4v8CuTJ","https://ap.wps.com/l/cbCailHws4v8CuTJ","pdf",1153068,1,11,"English","en",105,"# Introduction\n## Tipping points in nonlinear dynamical systems\n## Challenges compared with oscillatory critical transitions\n## Reservoir-computing framework for nonautonomous tipping\n## Application: predicting potential AMOC collapse","[{\"question\":\"What is a tipping point in the context of this study?\",\"answer\":\"A tipping point is a transition from one stable steady state to another. The change can be catastrophic and corresponds to system collapse in many settings.\"},{\"question\":\"Why is predicting tipping points harder than predicting other critical transitions?\",\"answer\":\"Near a tipping point, the dynamics become steady-state rather than oscillatory or chaotic. Without oscillatory time structure, the model has less obvious temporal variation to learn from.\"},{\"question\":\"How is the Atlantic Meridional Overturning Circulation (AMOC) used as an application?\",\"answer\":\"The framework is applied to forecasting a possible AMOC collapse. The predicted collapse window is based on synthetic and currently available empirical data and is consistent with results reported in the literature.\"}]","Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation - Abstract and introduction | PDF",1785935290,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-prediction-of-tipping-with-applications-to-the-atlantic-meridional-overturning-circulation-abstract-and-introduction","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-prediction-of-tipping-with-applications-to-the-atlantic-meridional-overturning-circulation-abstract-and-introduction/126864/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is a tipping point in the context of this study?","Question",{"text":75,"@type":76},"A tipping point is a transition from one stable steady state to another. The change can be catastrophic and corresponds to system collapse in many settings.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is predicting tipping points harder than predicting other critical transitions?",{"text":80,"@type":76},"Near a tipping point, the dynamics become steady-state rather than oscillatory or chaotic. Without oscillatory time structure, the model has less obvious temporal variation to learn from.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the Atlantic Meridional Overturning Circulation (AMOC) used as an application?",{"text":84,"@type":76},"The framework is applied to forecasting a possible AMOC collapse. The predicted collapse window is based on synthetic and currently available empirical data and is consistent with results reported in the literature.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]