[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122672-en":3,"doc-seo-122672-105":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},122672,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Detecting disturbances in network-coupled dynamical systems with machine learning","Identifying unknown disturbances in network-coupled dynamical systems without access to the disturbances or the underlying dynamics is critical for applications ranging across engineering, ecology, neuroscience, and other complex networks. A model-free machine-learning approach is presented, using reservoir computing trained only with observations under known forcing functions. The method locates the disturbed nodes and reconstructs disturbance time courses across linear and nonlinear examples, and demonstrates scalability to large networks via a pseudo-parallelization design.","arXiv :2307 . 1277 1v 1 [ cs .LG] 24 Jul 2023  \nDetecting disturbances in network-coupled dynamical systems with machine learning  \nPer Sebastian Skardal1, a) and Juan G. Restrepo2  \n1) Department of Mathematics, Trinity College, Hartford, CT 06106, USA  \n2) Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA  \nIdentifying disturbances in network-coupled dynamical systems without knowledge of the disturbances or underlying dynamics is a problem with a wide range of applications. For example, one might want to know which nodes in the network are being disturbed and identify the type of disturbance. Here we present a model-free method based on machine learning to identify such unknown disturbances based only on prior observations of the system when forced by a known training function. We 􀀌nd that this method is able to identify the locations and properties of many di􀀋erent types of unknown disturbances using a variety of known forcing functions. We illustrate our results both with linear and nonlinear disturbances using food web and neuronal activity models. Finally, we discuss how to scale our method to large networks.  \nDespite a wide range of potential applications, identifying disturbances made to networkcoupled dynamical systems is a di􀀎cult problem due to the complex nature of interactions between di􀀋erent units. Even a disturbance made to a single node can be challenging to localize due to the propagation of behavior through the network. Here we present a model-free method using machine learning techniques, speci􀀌cally reservoir computing, to identify disturbances to networkcoupled dynamical systems. This method assumes no knowledge of the underlying dynamics nor the disturbance itself. All that is needed is su􀀎cient observations of the system under the in-􀀍uence of a known forcing function. We show using examples from ecology and neuroscience that the method robustly identi􀀌es the disturbances made to the system for a relatively simple set of forcing functions used for training. Moreover, we show that the method is scalable to large networks using a pseudo-parallelization architecture.  \nI. INTRODUCTION  \nMachine learning techniques have proven to be extremely useful for data-driven modeling and prediction of complex systems 1–4 . In many of these applications, a machine learning system is trained to learn and replicate the dynamics of a nonlinear system from noisy or partially observed data, and then the machine learning system is used, for example, to forecast the dynamics5–8 , to estimate Lyapunov exponents9 or unstable periodic orbits 10 , to infer network coupling 11 , or to predict extreme events 12 and crises in non-stationary dynamical systems 13,14 .  \na) Electronic mail: [persebastian.skardal@trincoll.edu](persebastian.skardal@trincoll.edu)  \nMachine learning techniques can also be used without the need to replicate the intrinsic dynamics of the system. For example, Ref.15 uses reservoir computers, a particular class of machine learning systems suited to modeling time-dependent systems, to learn the response of dynamical systems to stimuli and then design data-driven control algorithms. In Ref.16 , we recently proposed a similar scheme to identify and suppress unknown disturbances to dynamical systems. Detecting disturbances to nonlinear dynamical systems is a crucial problem with a wide range of applications, e.g., in engineering, and in particular in power grid networks 17–23 , ecology24,25 ,􀀍uid dynamics 26,27 , and climate change28 . In this paper, we extend our results to the identi􀀌cation of disturbancesin network-coupled dynamical systems. Network-coupled systems present a particular challenge in identifying disturbances, as the ripple of an external force complicates the inference of both the location and nature of the disturbance22,29,30 . By extending the method presented in 16 to network-coupled dynamical systems, we are able to robustly identify which nodes a","cbCaitRIofkU660J","https://ap.wps.com/l/cbCaitRIofkU660J","pdf",1580893,1,9,"English","en",105,"# Introduction\n## Motivation and prior work\n## Problem statement and contributions\n# Problem statement and setup of the reservoir computer\n## System model\n# Example 1: linear disturbances to a food web\n# Example 2: nonlinear disturbances to excitatory-inhibitory neuron populations\n# Scalability to larger networks\n## Ensemble of node-specific reservoirs\n# Conclusion and discussion","[{\"question\":\"What problem does the method address in network-coupled dynamical systems?\",\"answer\":\"It identifies unknown disturbances affecting nodes in a network-coupled system without knowing the disturbances themselves or the underlying intrinsic dynamics.\"},{\"question\":\"What information is required to train the machine-learning model?\",\"answer\":\"Only sufficient observations collected while the system is forced by a known training function are required; the method is model-free regarding the disturbance and dynamics.\"},{\"question\":\"How does the approach handle scalability to large networks?\",\"answer\":\"It scales using a pseudo-parallelization architecture and an ensemble of node-specific reservoirs to manage many nodes efficiently.\"}]","Detecting disturbances in network-coupled dynamical systems with machine learning | PDF",1785812096,23,{"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},"detecting-disturbances-in-network-coupled-dynamical-systems-with-machine-learning","",{"@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/detecting-disturbances-in-network-coupled-dynamical-systems-with-machine-learning/122672/",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":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the method address in network-coupled dynamical systems?","Question",{"text":75,"@type":76},"It identifies unknown disturbances affecting nodes in a network-coupled system without knowing the disturbances themselves or the underlying intrinsic dynamics.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What information is required to train the machine-learning model?",{"text":80,"@type":76},"Only sufficient observations collected while the system is forced by a known training function are required; the method is model-free regarding the disturbance and dynamics.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the approach handle scalability to large networks?",{"text":84,"@type":76},"It scales using a pseudo-parallelization architecture and an ensemble of node-specific reservoirs to manage many nodes efficiently.","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},[93,97,101,105,110,115,120,123,127,130,134],{"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":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":21,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},"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"]