[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122459-en":3,"doc-seo-122459-105":29,"detail-sidebar-cat-0-en-105":90},{"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":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":26,"seo_description":14,"update_tm":27,"read_time":28},122459,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Predicting Chaotic System Behavior using Machine Learning Techniques","Machine learning methods, especially deep learning, have shown strong results for time series forecasting compared with traditional techniques in both single- and multi-variable settings. This work evaluates three approaches—next generation reservoir computing (NG-RC), reservoir computing (RC), and long short-term memory (LSTM)—for predicting chaotic dynamics. Experiments use time series from four representative chaotic systems: Lorenz, Rssler, Chen, and Qi. Performance is compared by accuracy, efficiency, and robustness, concluding NG-RC offers higher computational efficiency and greater predictive potential for chaotic system behavior.","Predicting Chaotic System Behavior using Machine  \nLearning Techniques  \nHuaiyuan Rao 1 , Yichen Zhao 1 , Qiang Lai2  \narXiv :2408 .05702v1 [ cs .LG] 11 Aug 2024  \nAbstract—Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable predictions. This study aims to investigate the capability of i) Next Generation Reservoir Computing (NG-RC) ii) Reservoir Computing (RC) iii) Long short-term Memory (LSTM) for predicting chaotic system behavior, and to compare their performance in terms of accuracy, efficiency, and robustness. These methods are applied to predict time series obtained from four representative chaotic systems including Lorenz, Rssler, Chen, Qi systems. In conclusion, we found that NG-RC is more computationally efficient and offers greater potential for predicting chaotic system behavior.  \nI. INTRODUCTION  \nTime series data have attracted significant attention across various fields in the natural and social sciences because of their potential applications. The analysis and prediction of time series data have been the focus of extensive research over the past few decades [1]–[5] . Chaotic time series are among the most complex because even small perturbation in initial values can lead to significant variations in their behaviors. Due to their sensitivity to initial conditions, it is a challenging task to predict chaotic time behaviors.  \nA practical solution is to develop models that forecast the behavior of chaotic time series. Recently, data-driven approaches such as machine learning (ML) have shown its efficiency on chaotic time series forecasting. For instance, recurrent neural networks (RNNs) are widely used across various fields in engineering and science for learning sequential tasks or modeling and predicting time series [6]–[8] . Yet, they struggle with long-term temporal dependencies, slow and subtle changes, or significantly varying time scales because their loss gradients backpropagated in time tend to saturate or diverge during training [9] . One solution to this is based on specifically designed RNN architectures with gating mechanisms, such as long short-term memory (LSTM) [10], which enables states from earlier time steps to more easily influence activities occurring much later by using a protected memory buffer.  \nReservoir computing (RC) has shown the potential of achieving higher-precision prediction of chaotic time series [11]–[13] . The core idea is to utilize dynamical systems as  \n1 School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30308, USA. {hrao43, [yzhao654](yzhao654}@gatech.edu)[}](yzhao654}@gatech.edu)[@gatech.edu](yzhao654}@gatech.edu)  \n2 School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China [laiqiang87@126.com](laiqiang87@126.com)  \nreservoirs (nonlinear generalizations of standard bases) to adaptively learn spatiotemporal features and hidden patterns in complex time series [14] . A RC model is based on a recurrent artificial neural network with a pool of interconnected neurons. To avoid the vanishing gradient problem during training, the RC paradigm randomly assigns the input-layer and reservoir link weights. Unlike other machine learning methods which are computational costly, only the weights of the output links are trained via a regularized linear least-squares optimization procedure. Due to its simple structure, this method has been used for multi-step-ahead predictions of nonlinear time series and for modeling chaotic dynamical systems with low computational cost [15]–[17] .  \nThe RCs have been developed from the original Echostate network (ESN)-based to nonlinear vector autoregression (NVAR), which also called NG-RC [18] . An NVAR machine is created where the feature vector is composed of time-delayed observations o","cbCaiaja7JzNIfcY","https://ap.wps.com/l/cbCaiaja7JzNIfcY","pdf",6006229,1,"English","en",105,"# Introduction\n## Problem Formulation\n## Modeling Approaches and Evaluation Metrics\n## Experimental Applications and Discussion\n## Conclusions","[{\"question\":\"What three machine learning methods are compared for chaotic time series prediction?\",\"answer\":\"The study compares NG-RC, reservoir computing (RC), and long short-term memory (LSTM) for predicting chaotic system behavior.\"},{\"question\":\"Which chaotic systems are used to generate the forecasting time series?\",\"answer\":\"Time series are obtained from four representative chaotic systems: Lorenz, Rssler, Chen, and Qi.\"},{\"question\":\"How does NG-RC perform compared with RC and LSTM?\",\"answer\":\"NG-RC is reported to be more computationally efficient and to offer greater potential for predicting chaotic system behavior, based on accuracy, efficiency, and robustness comparisons.\"}]","Predicting Chaotic System Behavior using Machine Learning Techniques | PDF",1785810760,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":23,"language":22,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"predicting-chaotic-system-behavior-using-machine-learning-techniques","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/predicting-chaotic-system-behavior-using-machine-learning-techniques/122459/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":22,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What three machine learning methods are compared for chaotic time series prediction?","Question",{"text":74,"@type":75},"The study compares NG-RC, reservoir computing (RC), and long short-term memory (LSTM) for predicting chaotic system behavior.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which chaotic systems are used to generate the forecasting time series?",{"text":79,"@type":75},"Time series are obtained from four representative chaotic systems: Lorenz, Rssler, Chen, and Qi.",{"name":81,"@type":72,"acceptedAnswer":82},"How does NG-RC perform compared with RC and LSTM?",{"text":83,"@type":75},"NG-RC is reported to be more computationally efficient and to offer greater potential for predicting chaotic system behavior, based on accuracy, efficiency, and robustness 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