Physics-Informed Neural Network for Inverse Design of Cylindrical Kresling Origami with Discrete Side Count Optimization

Physics-Informed Neural Network for Inverse Design of Cylindrical Kresling Origami with Discrete Side Count Optimization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Physics-Informed Neural Network for Inverse Design of Cylindrical Kresling Origami with Discrete Side Count Optimization Shijun Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9144582/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Origami mechanisms excel in space and material utilization, but their design variables involve the coupling of continuous and discrete variables, complicating reverse engineering—especially for polygons with dis crete side counts. Traditional numerical optimization methods struggle with discrete variables and lack automation. This paper proposes a Physics-Informed Neural Network (PINN) framework for the reverse engineering of Kresling origami. In this framework, the discrete side count *m* is first adjusted by a dis tance penalty to shorten the distance between the optimized and target values. This ensures contin uously differentiable gradients and smooth transitions, avoiding loss bounces. Then, a soft projection function (a softmax function with a learnable temperature) strictly constrains the output value to integers, ultimately achieving continuous differentiability. Physical constraints (potential energy difference and near zero torque, achieved through ∂U/∂β ≈ 0) are embedded in the loss function, enabling label-free training. Novel engineering constraints ensure manufacturability. Numerical examples show MSE of the energy curve 95% of runs. Cylindrical Kresling Physics-Informed Neural Network (PINN) Inverse design Machine learning Origami metamaterials Multistable structures Energy programming Differentiable discrete optimization Annealed softmax projection Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9144582","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":607349334,"identity":"a3ecc0be-6505-4fa3-b430-455e36438be4","order_by":0,"name":"Shijun Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVRIiWNgGAWjYBACeWbmww8+VNjY8TMcPkCcFsP2tjTDGWfSkiUbjyUQac2ZMwbSvG2HGTccPmNAnA7GGWkJhjPY0pgZjp35eOMNg52cbgMBLewSyQcefOCx4WPsObvZcg5DsrHZAaJskUhjZpY4u02ah+FA4jZCWhhu5BhI8xgcZmyTf/OMSC0g7/MkHGbsYTjDRpwWSCAfSEuWYDhmbDnHgAi/gKPy4z8bO/sDhx/eeFNhJ0dQCwqQ4CEyapC1kKpjFIyCUTAKRgQAAD7eSM/p5/EUAAAAAElFTkSuQmCC","orcid":"","institution":"Swinburne University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Shijun","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2026-03-17 06:07:53","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9144582/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9144582/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105033987,"identity":"78d2c51b-60e7-454c-8083-a2a1b37dda36","added_by":"auto","created_at":"2026-03-20 07:22:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2557824,"visible":true,"origin":"","legend":"","description":"","filename":"InverseDesignusingPINN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9144582/v1_covered_e1c68534-5434-43ab-ba18-1b4781dd093e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhysics-Informed Neural Network for Inverse Design of Cylindrical Kresling Origami with Discrete Side Count Optimization\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Cylindrical Kresling, Physics-Informed Neural Network (PINN), Inverse design, Machine learning, Origami metamaterials, Multistable structures, Energy programming, Differentiable discrete optimization, Annealed softmax projection","lastPublishedDoi":"10.21203/rs.3.rs-9144582/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9144582/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOrigami mechanisms excel in space and material utilization, but their design variables involve the coupling of continuous and discrete variables, complicating reverse engineering—especially for polygons with dis crete side counts. Traditional numerical optimization methods struggle with discrete variables and lack automation. This paper proposes a Physics-Informed Neural Network (PINN) framework for the reverse engineering of Kresling origami. In this framework, the discrete side count *m* is first adjusted by a dis tance penalty to shorten the distance between the optimized and target values. This ensures contin uously differentiable gradients and smooth transitions, avoiding loss bounces. Then, a soft projection function (a softmax function with a learnable temperature) strictly constrains the output value to integers, ultimately achieving continuous differentiability. Physical constraints (potential energy difference and near zero torque, achieved through ∂U/∂β ≈ 0) are embedded in the loss function, enabling label-free training. Novel engineering constraints ensure manufacturability. 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