[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126610-en":3,"doc-seo-126610-105":31,"detail-sidebar-cat-0-en-105":92},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126610,687207020761,"Patrick","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Prediction and identification of nonlinear dynamical systems using machine learning approaches","Nonlinear dynamical systems appear across industry, physics, engineering, biology, and social networks, yet reliable prediction and model identification from observational data remain difficult under noise and complex behavior. A machine learning framework named Runge–Kutta guided next-generation reservoir computing (RKNG-RC) is developed for chaotic systems including Lorenz63 and experimental cases such as chaotic Chua’s circuit. The method supports accurate prediction tasks and reconstructs governing ordinary differential equations with interpretability derived from trained weights, surpassing traditional black-box reservoir approaches. Numerical simulations and real experiments validate the approach and its robustness.","Journal of Industrial Information Integration 35 (2023) 100503  \n| Full length article\u003Cbr>Prediction and identification of nonlinear dynamical systems using machine learning approaches\u003Cbr>Leisheng Jin a, Zhuo Liu a, Lijie Lib,∗\u003Cbr>a College of Integrated Circuit Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu, China b College of Engineering, Swansea University, Swansea, SA1 8EN, Wales, United Kingdom |  |  |  |\n| --- | --- | --- | --- |\n| A R T I C L E I N F O |  | A B S T R A C T |  |\n| Keywords:\u003Cbr>Prediction\u003Cbr>Chaotic dynamical systems Identification\u003Cbr>Reservoir computing Runge–Kutta |  | Nonlinear dynamical systems are widely implemented in many areas. The prediction and identification of these dynamical systems purely based on observational data are of great significance for practical applications. In the work, we develop a machine learning based approach called Runge–Kutta guided next-generation reservoir computing (RKNG-RC). The proposed scheme can process data information generated by the most complicated nonlinear dynamical systems such as chaotic Lorenz63 system even with noise, and experimental systems such as chaotic Chua’s electronic circuit, showing an outstanding ability for prediction tasks. More importantly, the RKNG-RC is found to have distinctive interpretability that from the trained weights the ordinary differential equation governing the observable data can be deduced, which is beyond the processing capacities of traditional approaches. The work provides an efficient platform for processing information generated by various dynamical systems. |  |\n\n1. Introduction  \nThe prediction and identification of dynamical models that underpin systems in industry [1,2], physics [3], engineering [4], biology [5], and social network [6,7] has been an important and challenging topic. Most of traditional methods rely heavily on expert intuition and suffer a large computational cost. As a result, it is seen recently a focused attention on developing more efficient data-driven modeling methods [8–11]. Particularly, machine learning offers a shortcut for analyzing limited observational data and learning the underlying nonlinear dynamics [12–14]. Various of neural networks are proposed for discovering representations of complex systems, closure modeling and chaotic time-series prediction [15–17]. Among these, the reservoir computing (RC) [18], asa type of recurrent neural networks (RNN), is deemed as one of the most attractive platforms for processing information generated by various of dynamical systems [19–22].  \nThe RCs have been developed from the original Echo-state network (ESN)-based to the time-delayed based [23], and until recently the next generation of reservoir computing (NG-RC) [24]. The core idea of RCs is to map the limited state values (input) into a much higher dimensional networks realized by a reservoir, where the reservoir could be timedelayed, or constructed by randomly connected neurons, or replaced by specially designed feature vectors, and a weight matrix that couples the reservoir state and output layer is trained to find the desired function between the input and output. Previous studies have shown that RC  \n∗ Corresponding author.  \nE-mail addresses: [jinls@njupt.edu.cn](jinls@njupt.edu.cn) (L. Jin), [l.li@swansea.ac.uk](l.li@swansea.ac.uk) (L. Li).  \nis competent for tasks such as prediction of chaotic systems, reconstruction chaotic attractors, nonlinear behaviors controlling [21,25–28] etc. However, in general, there is a lack of interpretability of using RC in the sense that the RC behaves like a black-box having many hyperparameters to be adjusted. The trained RC can be seen as a datadriven model but it is failed to give explicit information about the mathematical structure behind the observable data.  \nIn this paper, we propose a new type of NG-RC based framework in which the structure construction is guided by Runge–Kutta algorithm and ","cbCailqx4TaALTnj","https://ap.wps.com/l/cbCailqx4TaALTnj","pdf",2637745,3,1,10,"English","en",105,"# Introduction\n## Background and motivation\n# Theories\n## Problem description","[{\"question\":\"What is RKNG-RC and what problem does it address?\",\"answer\":\"RKNG-RC is a machine learning approach for predicting and identifying nonlinear dynamical systems directly from observational data, including cases affected by noise and experimental measurement effects.\"},{\"question\":\"Which types of dynamical systems are demonstrated in the paper?\",\"answer\":\"The method is validated on chaotic Lorenz63 data (with and without noise) and on experimental chaotic Chua’s electronic circuit.\"},{\"question\":\"How does RKNG-RC provide interpretability compared with traditional reservoir computing?\",\"answer\":\"From the trained weights, RKNG-RC allows deduction of the ordinary differential equation governing the observable data, whereas conventional reservoir computing is often treated as a black box with many hyperparameters.\"}]","Prediction and identification of nonlinear dynamical systems using machine learning approaches | 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is RKNG-RC and what problem does it address?","Question",{"text":76,"@type":77},"RKNG-RC is a machine learning approach for predicting and identifying nonlinear dynamical systems directly from observational data, including cases affected by noise and experimental measurement effects.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which types of dynamical systems are demonstrated in the paper?",{"text":81,"@type":77},"The method is validated on chaotic Lorenz63 data (with and without noise) and on experimental chaotic Chua’s electronic circuit.",{"name":83,"@type":74,"acceptedAnswer":84},"How does RKNG-RC provide interpretability compared with traditional reservoir computing?",{"text":85,"@type":77},"From the trained weights, RKNG-RC allows deduction of the ordinary differential equation governing the observable data, whereas conventional reservoir computing is often treated as a black box with many 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