Enhanced Inverse Design of Thin-Film High Reflectors Using a Mixture Density Network and Optimization Framework

Enhanced Inverse Design of Thin-Film High Reflectors Using a Mixture Density Network and Optimization Framework | 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 Enhanced Inverse Design of Thin-Film High Reflectors Using a Mixture Density Network and Optimization Framework Adna Kumar, Shrakajana Gupta, Isha Patel, Aarav Sharma, Rohan Desai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5059338/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 Deep learning (DL) has emerged as a promising tool for photonic inverse design. Despite initial successes in retrieving spectra of modest complexity with near-instantaneous readout, DL-assisted design methods often exhibit lower accuracy compared to advanced optimization techniques and have yet to demonstrate competitiveness in handling spectra of practical relevance. In this work, we introduce a tandem optimization model that integrates a mixture density network (MDN) and a fully connected (FC) network to perform inverse design of practical thin-film high reflectors. The multimodal nature of the MDN provides access to a vast array of candidate designs described by probability distributions, which are iteratively sampled and evaluated by the FC network to facilitate rapid optimization. We demonstrate that the proposed model effectively retrieves the reflectance spectra of 20-layer thin-film structures. Notably, it reproduces high reflectors with periodic structures derived from physical principles with high precision, despite the absence of such information in the training data. Additionally, the model is capable of producing improved designs with extended high-reflectance zones. Our approach combines the high-efficiency advantages of DL with optimization-enabled performance improvements, making it an efficient and on-demand solution for practical inverse design applications. Materials Theory and Modeling Artificial Intelligence and Machine Learning artificial neural networks deep learning inverse design nanophotonics optimization thin-film optics 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. 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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-5059338","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":351622358,"identity":"1c90c971-1eb2-4a07-b581-3421d9886b8f","order_by":0,"name":"Adna Kumar","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Adna","middleName":"","lastName":"Kumar","suffix":""},{"id":351622359,"identity":"838c3e62-7be0-49fe-9eba-cd37696bdf29","order_by":1,"name":"Shrakajana Gupta","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Shrakajana","middleName":"","lastName":"Gupta","suffix":""},{"id":351622360,"identity":"9cd86c9d-73ae-47bc-af3a-015ae3d04e32","order_by":2,"name":"Isha Patel","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Isha","middleName":"","lastName":"Patel","suffix":""},{"id":351622361,"identity":"6ffa8248-ed4a-4d91-889b-1b358de27b7b","order_by":3,"name":"Aarav Sharma","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Aarav","middleName":"","lastName":"Sharma","suffix":""},{"id":351622362,"identity":"9fd8f7cf-46d9-4a31-a899-50261e0bba45","order_by":4,"name":"Rohan Desai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYFACHhDBDMSMDQYfDCTAYhJgRIyWwhkkamFg+MwDFcOnnsG8vffg5wIGazn59sONm20KLOz5G5gP3uZhsMjDpUXmzLlk6RkM6cYGZxKbjXMMJBJnHGBLtuZhkCjGpUVCIsdAmofhcOIGhsQ2kJYEAwYeM6CIRGIDbi3Gv4Fa6uf3P2z/bWEgYW/AwP+NkBaQmYcTGG4kNhgzGEgwbmDgYcOvheeMmTWPQbrhhhsPGwx7QH45zGZsOccAjxb2HuPbPBXW8vL96Q8Mfvyps+dvb354401FHU4tEGCAzGHGEBkFo2AUjIJRQCoAAOFaRtu2eBvsAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Rohan","middleName":"","lastName":"Desai","suffix":""}],"badges":[],"createdAt":"2024-09-09 16:11:14","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-5059338/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5059338/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":64203479,"identity":"55adb9ba-c8a5-48fa-a043-447ee14fe5f2","added_by":"auto","created_at":"2024-09-10 03:36:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":485039,"visible":true,"origin":"","legend":"","description":"","filename":"EnhancedInverseDesignofThinFilmHighReflectorsUsingaMixtureDensityNetworkandOptimizationFramework.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5059338/v1_covered_19cb63f4-d0d5-4ba3-b3c1-9d37ea198b34.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEnhanced Inverse Design of Thin-Film High Reflectors Using a Mixture Density Network and Optimization Framework\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":"artificial neural networks, deep learning, inverse design, nanophotonics, optimization, thin-film optics","lastPublishedDoi":"10.21203/rs.3.rs-5059338/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5059338/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDeep learning (DL) has emerged as a promising tool for photonic inverse design. Despite initial successes in retrieving spectra of modest complexity with near-instantaneous readout, DL-assisted design methods often exhibit lower accuracy compared to advanced optimization techniques and have yet to demonstrate competitiveness in handling spectra of practical relevance. In this work, we introduce a tandem optimization model that integrates a mixture density network (MDN) and a fully connected (FC) network to perform inverse design of practical thin-film high reflectors. The multimodal nature of the MDN provides access to a vast array of candidate designs described by probability distributions, which are iteratively sampled and evaluated by the FC network to facilitate rapid optimization.\u0026nbsp;We demonstrate that the proposed model effectively retrieves the reflectance spectra of 20-layer thin-film structures. 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