[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120789-en":3,"doc-seo-120789-105":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":20,"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},120789,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Controlling dynamical systems to complex target states using machine learning - next-generation vs. classical reservoir computing","Machine learning–based control of nonlinear dynamical systems enables steering behavior beyond simple periodic motion toward complex, user-defined target dynamics. The approach depends on training a model to reproduce the target dynamics with sufficient fidelity. Using a Lorenz-system example, chaotic parametrization is forced into intermittent dynamics, where classical reservoir computing is shown to perform effectively. A subsequent comparison introduces next-generation reservoir computing and evaluates performance under varying training-data budgets.","2023 International Joint Conference on Neural Networks (IJCNN) | 978-1-6654-8867-9/23/$31.00 ©2023 IEEE | DOI: 10. 1 109/ IJCNN54540. 2023. 10191257  \nControlling 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 Koeglmayr Institut fu¨r KI Sicherheit  \nDeutsches Zentrum fu¨r Luft- und Raumfahrt (DLR) Ulm, Germany [daniel.koeglmayr@dlr.de](daniel.koeglmayr@dlr.de)  \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 ta","cbCaipQKqlVUKLSm","https://ap.wps.com/l/cbCaipQKqlVUKLSm","pdf",2186923,1,7,"English","en",105,"# Abstract\n# Introduction\n# Controlling Chaos","[{\"question\":\"What is the goal of controlling dynamical systems in this work?\",\"answer\":\"The work aims to steer nonlinear dynamical systems into complex target states, not only into simple periodic behavior.\"},{\"question\":\"How does the reservoir-computing control mechanism determine the control force?\",\"answer\":\"It compares the actual trajectory under the new state to a hypothetical trajectory predicted as if the system stayed in the original target state, then computes the force from their difference.\"},{\"question\":\"What advantage does next-generation reservoir computing provide over classical reservoir computing?\",\"answer\":\"With typical training data they offer comparable performance, but next-generation reservoir computing significantly outperforms when only very limited training data are available.\"}]","Controlling dynamical systems to complex target states using machine learning - next-generation vs. classical reservoir computing | PDF",1785732040,18,{"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/120789/",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":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the goal of controlling dynamical systems in this work?","Question",{"text":75,"@type":76},"The work aims to steer nonlinear dynamical systems into complex target states, not only into simple periodic behavior.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the reservoir-computing control mechanism determine the control force?",{"text":80,"@type":76},"It compares the actual trajectory under the new state to a hypothetical trajectory predicted as if the system stayed in the original target state, then computes the force from their difference.",{"name":82,"@type":73,"acceptedAnswer":83},"What advantage does next-generation reservoir computing provide over classical reservoir computing?",{"text":84,"@type":76},"With typical training data they offer comparable performance, but next-generation reservoir computing significantly outperforms when only very limited training data are available.","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"]