[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120718-en":3,"doc-seo-120718-105":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},120718,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Controlling dynamical systems to complex target states using machine learning - next-generation vs. classical reservoir computing","Controlling nonlinear dynamical systems with machine learning enables steering beyond simple periodic behavior toward complex, arbitrary target dynamics. Effective control requires training that reproduces the desired dynamics with sufficient fidelity. Using a case study of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, the work shows classical reservoir computing performs strongly. It then compares this with next-generation reservoir computing under different training-data budgets, finding similar accuracy for typical data volumes but clear superiority of next-generation RC under severe data scarcity.","Controlling dynamical systems to complex target states using machine learning: next-generation vs . classical reservoir computing  \n1st Alexander Haluszczynski risklab Allianz Global Investors Munich, Germany  \n[alexander.haluszczynski@gmail.com](alexander.haluszczynski@gmail.com)  \n2nd Daniel Kglmayr Institut fu¨r KI Sicherheit  \nDeutsches Zentrum fu¨r Luft- und Raumfahrt (DLR) Ulm, Germany [daniel.koeglmayr@dlr.de](daniel.koeglmayr@dlr.de)  \narXiv :2307 .07 195v 1 [ cs .LG] 14 Jul 2023  \n3rd Christoph Rth  \nInstitut fu¨r KI Sicherheit Deutsches Zentrum fu¨r Luft- und Raumfahrt (DLR) Ulm, Germany  \n[christoph.raeth@dlr.de](christoph.raeth@dlr.de)  \nAbstract—Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be trained to reproduce the target dynamics sufficiently well. On the example of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, we show first that classical reservoir computing excels at this task. In a next step, we compare those results based on different amounts of training data to an alternative setup, where next-generation reservoir computing is used instead. It turns out that while delivering comparable performance for usual amounts of training data, next-generation RC significantly outperforms in situations where only very limited data is available. This opens even further practical control applications in real world problems where data is restricted.  \nIndex Terms—control, chaos, dynamical systems, reservoir computing  \nI. INTRODUCTION  \nIt has been a significant breakthrough to be able to control chaotic systems into stable dynamical states [19], [24] . Classical approaches include delayed feedback control [20] as well as OGY control [19] where a system in a chaotic state is driven into a fixed point or periodic orbit by applying an external force. While most approaches were only able to control systems into rather simple dynamical states, it has been shown recently that more complex target states can be achieved by leveraging a machine learning based control mechanism [11] without requiring knowledge of the underlying equations. In order to derive the control force, a good prediction of the desired dynamics is needed.  \nThere has been remarkable progress made in the prediction of chaotic systems in the recent past with reservoir computing standing (RC) out [14], [18] delivering high accuracy predictions while being less data hungry than comparable methods  \ndue to its efficient architecture. There have been many advances and refinements of RC (e.g. see [4], [6],[15]) mounting to the recent proposal of next-generation reservoir computing (NG-RC) [7], where the randomly generated underlying neural network function is replaced by a determined polynomial multiplication rule of time-shifted inputs.  \nIn this study we compare the results of the reservoir computing powered control mechanism [11] to a similar setup, where next-generation reservoir computing is used [instead. it](instead. it)[ ](instead. it)is shown that the required amount of training data can be significantly lowered roughly by a factor of 10 . Requiring only very few training data, this approach becomes feasible for even more potential practical applications.  \nII. CONTROLLING CHAOS  \nThe original idea of chaos control is that unstable periodic orbits can be stabilized by small perturbations of the system resulting from applying an external force. Traditional approaches like OGY control [19] and delayed feedback control [20] either require knowledge of the underlying equations of the system or large amounts of data due to relying on phase space methods. Furthermore, it is only possible to control the system in simple dynamical target states. While there are many extensions [2] including a way to ”chaotify” periodic or synchronized dynamics [","cbCaiooZCTRjYPYg","https://ap.wps.com/l/cbCaiooZCTRjYPYg","pdf",1094261,1,7,"English","en",105,"# Abstract\n# Index Terms\n# I. Introduction\n# II. Controlling Chaos","[{\"question\":\"What problem does the document address in controlling dynamical systems?\",\"answer\":\"It addresses how to control nonlinear dynamical systems from chaotic behavior into more complex target states using machine learning, not only simple periodic motions.\"},{\"question\":\"How does classical reservoir computing help in the proposed control approach?\",\"answer\":\"Classical reservoir computing is trained to reproduce the target dynamics and then enables prediction of the hypothetical trajectory so a control force can be computed from the difference between actual and predicted evolution.\"},{\"question\":\"What advantage does next-generation reservoir computing provide?\",\"answer\":\"Next-generation reservoir computing matches classical RC for usual training-data amounts but significantly outperforms it when only very limited training data are available, making data-restricted practical control more feasible.\"}]","Controlling dynamical systems to complex target states using machine learning - next-generation vs. classical reservoir computing | PDF",1785731687,18,{"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},"controlling-dynamical-systems-to-complex-target-states-using-machine-learning-next-generation-vs-classical-reservoir-computing","",{"@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/controlling-dynamical-systems-to-complex-target-states-using-machine-learning-next-generation-vs-classical-reservoir-computing/120718/",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","2026-08-03",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 problem does the document address in controlling dynamical systems?","Question",{"text":75,"@type":76},"It addresses how to control nonlinear dynamical systems from chaotic behavior into more complex target states using machine learning, not only simple periodic motions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does classical reservoir computing help in the proposed control approach?",{"text":80,"@type":76},"Classical reservoir computing is trained to reproduce the target dynamics and then enables prediction of the hypothetical trajectory so a control force can be computed from the difference between actual and predicted evolution.",{"name":82,"@type":73,"acceptedAnswer":83},"What advantage does next-generation reservoir computing provide?",{"text":84,"@type":76},"Next-generation reservoir computing matches classical RC for usual training-data amounts but significantly outperforms it when only very limited training data are available, making data-restricted practical control more feasible.","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},[93,97,101,105,110,115,119,122,127,130,134],{"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":21,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]