[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127368-en":3,"doc-seo-127368-105":30,"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":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},127368,962085564549,"Genevieve","https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Exploring Non-Linear Dynamical Structure for Knee Kinematics Using Machine Learning","Human gait involves complex coordination across multiple limbs, with knee motion exhibiting nonlinear dynamical behavior that linear models cannot capture. This study applies advanced machine learning by combining the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm with Python to derive governing equations for knee movement during walking. Infrared marker data from a single subject’s knees during normal gait were used, and PySINDy identified dynamical system coefficients. Results highlight the usefulness of SINDy for revealing nonlinear dynamical structure in movement science.","Chapman University Digital Commons  \n\n| Physical Therapy Faculty Articles and Research | Physical Therapy |\n| --- | --- |\n| 12-2023\u003Cbr>Exploring Non-Linear Dynamical Structure for Knee Kinematics Using Machine Learning\u003Cbr>Liora Mayats-Alpay Rahul Soangra\u003Cbr>Follow this and additional works at: [https://digitalcommons.chapman.edu/pt_articles](https://digitalcommons.chapman.edu/pt_articles)\u003Cbr> Part of the Artificial Intelligence and Robotics Commons, and the Other Rehabilitation and Therapy Commons |  |\n\nExploring Non-Linear Dynamical Structure for Knee Kinematics Using Machine Learning  \nComments  \nThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in 2023 International Conference on Next Generation Electronics (NEleX). This article may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at [https://doi.org/10.1109/nelex59773.2023.10421398](https://doi.org/10.1109/nelex59773.2023.10421398) .  \nCopyright  \nIEEE  \nAuthor Manuscript Author Manuscript Author Manuscript Author Manuscript  \n\n|  | HHS Public Access\u003Cbr>Author manuscript\u003Cbr>2023 Int Conf Next Gener Electron NEleX (2023). Author manuscript; available in PMC 2025 June 18. |\n| --- | --- |\n\nPublished in final edited form as:  \n2023 Int Conf Next Gener Electron NEleX (2023). 2023 December ; 2023: . doi:10.1109/ nelex59773 .2023.10421398.  \nExploring Non-linear Dynamical Structure for Knee Kinematics Using Machine Learning  \nLiora Mayats-Alpay,  \nComputational and Data Sciences, Schmid College of Science and Technology, Chapman University, Orange 92866, CA, USA  \nRahul Soangra  \nCrean College of Health and Behavioral Sciences, Fowler School of Engineering Chapman University, Orange 92866, CA, USA  \nAbstract  \nHuman movement involves complex coordination between multiple limbs during execution.  \nHuman gait is cyclic, and the knee’s movement inherently follows nonlinear dynamic behavior that linear models cannot adequately capture. In this study, advanced Machine Learning (ML) techniques were employed to combine the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm using Python to reveal governing equations of knee movement during walking. We gathered a single subject’s knee motion data using infrared markers during normal walking. We utilized the PySINDy library to determine the governing equations and calculated the coefficient of dynamical systems associated with knee kinematics. Our results emphasize governing equations of dynamic systems in gait, particularly the knee kinematics during walking. We found that the SINDy algorithms could effectively reveal nonlinear dynamic systems in movement science.  \nKeywords  \nPySINDy; SINDy; Machine Learning; knee angle; dynamical system; governing equations;  \noptimization  \nI. INTRODUCTION  \nHuman walking is complex, especially the knee movement, which is associated with nonlinear chaotic structure. Dynamic knee kinematics involves a chaotic behavior similar to physics, biomechanics, and engineering fields [1] [5] [6] [7] [8] . Knee movement has received particular attention in movement science, with gait research contributing to various fields of injury, rehabilitation, orthopedics, sports medicine, neuroscience, and science in general [2] [9] [11] [16]. The chaotic behavior of the knee joint may be attributed to the involvement of musculoskeletal and nervous systems, but underlying motor control and governing equations have not been well characterized. The revolutionary growth of modern technology using Machine Learning (ML) makes it possible to process a large amount  \n[mayatsalpay@chapman.edu](mayatsalpay@chapman.edu) .  \nAuthor Manuscript Author Manuscript Author Manuscript Author Manuscript  \nMayats-Alpay and Soangra Page 2  \nof data, especially movement data or, in other words, drive data, which is essential in solving movement complexity [10] [12] [15] . While the complex kinematics of the knee come to the front ","cbCairQpa0s9vJr6","https://ap.wps.com/l/cbCairQpa0s9vJr6","pdf",2774650,1,18,"English","en",105,"# Abstract\n# Introduction\n# Methods and Data\n## Data","[{\"question\":\"What problem does the study address about knee movement?\",\"answer\":\"Knee motion during walking follows nonlinear dynamical behavior, and linear models cannot adequately capture the underlying structure. The study aims to characterize governing equations for this dynamics.\"},{\"question\":\"Which machine learning approach is used to extract governing equations?\",\"answer\":\"The study uses the SINDy algorithm combined with Python, implemented via the PySINDy library, to reveal governing equations from knee motion data.\"},{\"question\":\"How was the knee kinematics data collected and analyzed?\",\"answer\":\"Infrared markers were used to collect knee motion data during normal walking for a single subject. PySINDy was then applied to determine governing equations and related dynamical system coefficients.\"}]","Exploring Non-Linear Dynamical Structure for Knee Kinematics Using Machine Learning | PDF",1785938534,45,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"exploring-non-linear-dynamical-structure-for-knee-kinematics-using-machine-learning","",{"@graph":36,"@context":86},[37,54,69],{"@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/exploring-non-linear-dynamical-structure-for-knee-kinematics-using-machine-learning/127368/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-22","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the study address about knee movement?","Question",{"text":76,"@type":77},"Knee motion during walking follows nonlinear dynamical behavior, and linear models cannot adequately capture the underlying structure. The study aims to characterize governing equations for this dynamics.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which machine learning approach is used to extract governing equations?",{"text":81,"@type":77},"The study uses the SINDy algorithm combined with Python, implemented via the PySINDy library, to reveal governing equations from knee motion data.",{"name":83,"@type":74,"acceptedAnswer":84},"How was the knee kinematics data collected and analyzed?",{"text":85,"@type":77},"Infrared markers were used to collect knee motion data during normal walking for a single subject. 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