[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122721-en":3,"doc-seo-122721-105":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},122721,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","TASKS MAKYTH MODELS - Machine Learning Assisted Surrogates for Tipping Points - A Preprint","A machine learning (ML)-assisted framework links manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling to identify tipping points and quantify rare-event probabilities in complex systems. Using an event-driven stochastic agent-based model of trader mimetic behavior in a financial market, the work builds reduced-order models from high-dimensional spatiotemporal data. Models target mesoscopic Integro-Partial Differential Equations and latent-space mean-field Stochastic Differential Equations near the tipping point, comparing model choices and learning effort.","arXiv :2309 . 14334v1 [ cs .LG] 25 Sep 2023  \nTASKS MAKYTH MODELS: MACHINE LEARNING ASSISTED  \nSURROGATES FOR TIPPING POINTS  \nA PREPRINT  \nGianluca Fabiani 1 ,2 , Nikolaos Evangelou2 , Tianqi Cui2 , Juan M. Bello-Rivas2 , Cristina Martin-Linares3 , Constantinos Siettos4 , ∗ , Ioannis G. Kevrekidis2 ,5 ,6 ,†  \n(1) Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale, Naples 80138, Italy  \n(2)Dept. of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA  \n(3)Dept. of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA  \n(4)Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universita` degli Studi di Napoli Federico II, Naples 80126, Italy  \n(5)Dept. of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA  \n(6) School of Medicine’s Dept. of Urology, Johns Hopkins University, Baltimore, MD 21218, USA  \nSeptember 26, 2023  \nABSTRACT  \nWe present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them. Our illustrative example is an event-driven, stochastic agentbased model (ABM) describing the mimetic behavior of traders in a simple financial market. Given high-dimensional spatiotemporal data –generated by the stochastic ABM– we construct reducedorder models for the emergent dynamics at different scales: (a) mesoscopic Integro-Partial Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential Equations (SDEs) embedded in a low-dimensional latent space, targeted to the neighborhood of the tipping point. We contrast the uses of the different models and the effort involved in learning them.  \nKeywords Machine Learning · Tipping Points · Complex Systems · Reduced Order Models · Rare Event Analysis · Integro-Partial Differential Equations · Stochastic Differential Equations  \n1 Introduction  \nComplex systems are typically characterized by the occurrence of phenomena at multiple scales: from the microscopic scale, where individual units evolve and interact among themselves, to the mesoscopic and macroscopic scales, where the emergent properties arise, and where system level modelling, numerical analysis, prediction, optimization and control is desired [1, 2] . Interactions at the microscopic/individual scale may trigger abrupt changes (rare events) in the emergent dynamics, which can lead to catastrophic shifts/major irreversible changes in the dominant mesoscopic/ macroscopic spatio-temporal behavioral pattern. Such sudden major changes occur with higher probability near socalled tipping points [3, 4, 5, 6, 7, 8], which are most often associated with bifurcation points in nonlinear dynamics terminology. The computation of the frequency/probability of occurrence of such transitions, and the detection of the corresponding tipping points that underpin them, is of critical importance in many real-world systems ranging from financial markets, social dynamics and power networks to biological and environmental ones. Our need for understanding the behavior of such systems has made Agent-Based Models (ABMs) a key modeling tool for “creating  \n∗ Corresponding author, email: [constantinos.siettos@unina.it](constantinos.siettos@unina.it)[ ](constantinos.siettos@unina.it)†Corresponding author, email: [yannisk@jhu.edu](yannisk@jhu.edu)  \nsurrogate versions of real-world complex systems inside our computing machines, changing the way we do science”[9, 10] .  \nWhen detailed high-fidelity microscopic/atomistic simulators are available, modeling practice often involves performing extensive, brute-force temporal simulations to estimate the frequency distribution of such transitions [11, 12, 13] . This direct initial approach is neither systematic nor compu","cbCais3dmvNBiiJD","https://ap.wps.com/l/cbCais3dmvNBiiJD","pdf",1803442,1,29,"English","en",105,"# Introduction\n## Multi-scale dynamics and tipping points\n## Rare-event estimation and limitations of brute-force simulation\n## Collective variables and manifold learning\n## Reduced-order model construction and inverse problem","[{\"question\":\"What is the document’s main goal for complex systems?\",\"answer\":\"Detect tipping points in emergent behavior and characterize the probabilities of rare events near them using a machine learning assisted multiscale framework.\"},{\"question\":\"Which modeling approach is used as an illustrative example?\",\"answer\":\"An event-driven stochastic agent-based model describing traders’ mimetic behavior in a simple financial market.\"},{\"question\":\"How are reduced-order models constructed from high-dimensional data?\",\"answer\":\"The method constructs models at different scales from spatiotemporal data, including mesoscopic Integro-Partial Differential Equations and latent-space mean-field-type Stochastic Differential Equations targeted near the tipping point.\"}]","TASKS MAKYTH MODELS - Machine Learning Assisted Surrogates for Tipping Points - A Preprint | PDF",1785812524,73,{"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},"tasks-makyth-models-machine-learning-assisted-surrogates-for-tipping-points-a-preprint","",{"@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/tasks-makyth-models-machine-learning-assisted-surrogates-for-tipping-points-a-preprint/122721/",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","2026-08-04",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 the document’s main goal for complex systems?","Question",{"text":75,"@type":76},"Detect tipping points in emergent behavior and characterize the probabilities of rare events near them using a machine learning assisted multiscale framework.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which modeling approach is used as an illustrative example?",{"text":80,"@type":76},"An event-driven stochastic agent-based model describing traders’ mimetic behavior in a simple financial market.",{"name":82,"@type":73,"acceptedAnswer":83},"How are reduced-order models constructed from high-dimensional data?",{"text":84,"@type":76},"The method constructs models at different scales from spatiotemporal data, including mesoscopic Integro-Partial Differential Equations and latent-space mean-field-type Stochastic Differential Equations targeted near the tipping point.","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"]