{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T14:46:28Z","timestamp":1792334788252,"version":"4.4.0"},"reference-count":218,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T00:00:00Z","timestamp":1792281600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T00:00:00Z","timestamp":1792281600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100032827","name":"Advanced Research and Invention Agency","doi-asserted-by":"publisher","award":["SMRB\u2010PR01\u2010P17"],"award-info":[{"award-number":["SMRB\u2010PR01\u2010P17"]}],"id":[{"id":"10.13039\/100032827","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["advanced.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Advanced Science"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Soft manipulators offer a route to safer, more adaptive and physically intelligent robots, but their compliant bodies remain difficult to model, predict and control. Large deformation, distributed actuation, hysteresis, material variability and contact\u2010rich interaction challenge both classical mechanics\u2010based models and purely data\u2010driven approaches. Here, we examine emerging modeling perspectives for soft manipulators through a conceptual progression from sparse identification of nonlinear dynamics to hybrid intelligence. We discuss how sparse identification of nonlinear dynamics (SINDy), Koopman learning, neural ordinary differential equations, physics\u2010informed neural networks, and hybrid physics machine learning models contribute complementary capabilities, including interpretable reduced\u2010order dynamics, control\u2010ready prediction, continuous\u2010time latent modeling, physics\u2010constrained field reconstruction, and residual correction. We present that no single modeling approach is sufficient for the next generation of soft robotic systems. Instead, progress requires integrated modeling ecosystems that combine mechanical structure, data\u2010driven discovery and task\u2010aware adaptation. Such hybrid\u2010intelligence frameworks can transform models from passive descriptions of deformation into active components of sensing, control, design and decision\u2010making, enabling soft manipulators that are more interpretable, robust and deployable in real\u2010world\u00a0environments.<\/jats:p>","DOI":"10.1002\/advs.78334","type":"journal-article","created":{"date-parts":[[2026,10,18]],"date-time":"2026-10-18T14:32:11Z","timestamp":1792333931000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data\u2010Driven and Physics\u2010Informed Modeling Perspectives for Soft Manipulators: From SINDy to Hybrid Intelligence"],"prefix":"10.1002","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2680-3091","authenticated-orcid":false,"given":"Wenbo","family":"Hui","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering University of Bath Bath UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-4757-5030","authenticated-orcid":false,"given":"Yunyi","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering University of Bath Bath UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Teng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering University of Bath Bath UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1026-0482","authenticated-orcid":false,"given":"Yang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering University of Bath Bath UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2901-3388","authenticated-orcid":false,"given":"Min","family":"Pan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering University of Bath Bath UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,18]]},"reference":[{"issue":"3","key":"e_1_2_10_2_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/11762320802557865","article-title":"Soft Robotics: Biological Inspiration, State of the Art, and Future Research","volume":"5","author":"Trivedi D.","year":"2008","journal-title":"Applied Bionics and Biomechanics"},{"issue":"1","key":"e_1_2_10_3_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1089\/soro.2013.0001","article-title":"Soft Robotics: A Perspective\u2014Current Trends and Prospects for the Future","volume":"1","author":"Majidi C.","year":"2014","journal-title":"Soft Robotics"},{"issue":"5","key":"e_1_2_10_4_1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.tibtech.2013.03.002","article-title":"Soft Robotics: A Bioinspired Evolution in Robotics","volume":"31","author":"Kim S.","year":"2013","journal-title":"Trends in Biotechnology"},{"issue":"7553","key":"e_1_2_10_5_1","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1038\/nature14543","article-title":"Design, Fabrication, and Control of Soft Robots","volume":"521","author":"Rus D.","year":"2015","journal-title":"Nature"},{"issue":"1","key":"e_1_2_10_6_1","doi-asserted-by":"crossref","DOI":"10.1126\/scirobotics.aah3690","article-title":"Soft Robotics: Technologies and Systems Pushing the Boundaries of Robot Abilities","volume":"1","author":"Laschi C.","year":"2016","journal-title":"Science Robotics"},{"issue":"12","key":"e_1_2_10_7_1","doi-asserted-by":"crossref","DOI":"10.1002\/adem.201700016","article-title":"Soft Robotics: Review of Fluid\u2010Driven Intrinsically Soft Devices; Manufacturing, Sensing, Control, and Applications in Human\u2010Robot Interaction","volume":"19","author":"Polygerinos P.","year":"2017","journal-title":"Advanced Engineering Materials"},{"issue":"6","key":"e_1_2_10_8_1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1038\/s41578-018-0022-y","article-title":"Biomedical Applications of Soft Robotics","volume":"3","author":"Cianchetti M.","year":"2018","journal-title":"Nature Reviews Materials"},{"issue":"29","key":"e_1_2_10_9_1","doi-asserted-by":"crossref","DOI":"10.1002\/adma.201707035","article-title":"Soft Robotic Grippers","volume":"30","author":"Shintake J.","year":"2018","journal-title":"Advanced Materials"},{"issue":"13","key":"e_1_2_10_10_1","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1177\/0278364910368147","article-title":"Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review","volume":"29","author":"Webster R. 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