Inverse Binary Optimization of Convolutional Neural Network in Active Learning Efficiently Designs Nanophotonic Structures

Inverse Binary Optimization of Convolutional Neural Network in Active Learning Efficiently Designs Nanophotonic Structures | 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 Article Inverse Binary Optimization of Convolutional Neural Network in Active Learning Efficiently Designs Nanophotonic Structures Jaehyeon Park, Zhihao Xu, Gyeong-Moon Park, Tengfei Luo, Eungkyu Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5999417/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract Binary optimization using active learning schemes has gained attention for automating the discovery of optimal designs in nanophotonic structures and material configurations. Recently, active learning has utilized factorization machines (FM), which usually are second-order models, as surrogates to approximate the hypervolume of the design space, benefiting from rapid optimization by Ising machines such as quantum annealing (QA). However, due to their second-order nature, FM-based surrogate functions struggle to fully capture the complexity of the hypervolume. In this paper, we introduce an inverse binary optimization (IBO) scheme that optimizes a surrogate function based on a convolutional neural network (CNN) within an active learning framework. The IBO method employs backward error propagation to optimize the input binary vector, minimizing the output value while maintaining fixed parameters in the pre-trained CNN layers. We conduct a benchmarking study of the CNN-based surrogate function within the CNN-IBO framework by optimizing nanophotonic designs (e.g., planar multilayer and stratified grating structure) as a testbed. Our results demonstrate that CNN-IBO achieves optimal designs with fewer actively accumulated training data than FM-QA, indicating its potential as a powerful and efficient method for binary optimization. Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics Physical sciences/Engineering/Electrical and electronic engineering Binary optimization Active learning Convolutional Neural Network Inverse Optimization Nanophotonics Full Text Additional Declarations No competing interests reported. Supplementary Files SciRptrevisedSupportingInfo202503281259final.docx Cite Share Download PDF Status: Published Journal Publication published 30 Apr, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Accepted 21 Apr, 2025 Reviews received at journal 21 Apr, 2025 Reviews received at journal 20 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 09 Apr, 2025 Reviewers agreed at journal 08 Apr, 2025 Reviewers invited by journal 07 Apr, 2025 Submission checks completed at journal 05 Apr, 2025 First submitted to journal 28 Mar, 2025 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-5999417","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":440596919,"identity":"a5eaae7f-fccf-4ca6-abe8-09f7ef970e07","order_by":0,"name":"Jaehyeon Park","email":"","orcid":"","institution":"Kyung Hee University","correspondingAuthor":false,"prefix":"","firstName":"Jaehyeon","middleName":"","lastName":"Park","suffix":""},{"id":440596920,"identity":"0c67c351-2acb-4c32-b72c-75a4d1b94395","order_by":1,"name":"Zhihao Xu","email":"","orcid":"","institution":"University of Notre Dame","correspondingAuthor":false,"prefix":"","firstName":"Zhihao","middleName":"","lastName":"Xu","suffix":""},{"id":440596921,"identity":"d6aa693d-c874-482e-8269-dde1d6ea0912","order_by":2,"name":"Gyeong-Moon Park","email":"","orcid":"","institution":"Korea University","correspondingAuthor":false,"prefix":"","firstName":"Gyeong-Moon","middleName":"","lastName":"Park","suffix":""},{"id":440596922,"identity":"12363148-99c5-47f6-88dd-e1a90d53e5f4","order_by":3,"name":"Tengfei Luo","email":"","orcid":"","institution":"University of Notre Dame","correspondingAuthor":false,"prefix":"","firstName":"Tengfei","middleName":"","lastName":"Luo","suffix":""},{"id":440596923,"identity":"4d9f3bb4-8511-4ae9-8562-6ca04105d516","order_by":4,"name":"Eungkyu Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVRIiWNgGAWjYDACdjBpY2AA4SYQoYUZrDCNdC2HSdDCz8x88OHPH+eNzSUSGD/8YEjLJ6hFspkt2Zgn4baZ5YwEZskehhzLBkJaDA7zmEkzJNy2MbiRwCDNwFBhQNAW+8P833/+SDgH0sL8mygtBsw8bAw8CQfMgFrYgLbkENYicZjNWJonLdnY4MzDNssegzTCWvjbmx9+/GFjZ7jhePLhGz8qkglrQQKMDUB3kqJhFIyCUTAKRgFOAABkLzRITsRiywAAAABJRU5ErkJggg==","orcid":"","institution":"Kyung Hee University","correspondingAuthor":true,"prefix":"","firstName":"Eungkyu","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2025-02-10 13:08:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5999417/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5999417/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-99570-z","type":"published","date":"2025-04-30T15:57:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":81987841,"identity":"f45ac811-5440-422e-8dfd-f442d118c39b","added_by":"auto","created_at":"2025-05-05 16:06:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1181710,"visible":true,"origin":"","legend":"","description":"","filename":"SciRptrevisedmanuscript202503281259final.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5999417/v1_covered_9fd1376c-b7ab-46ae-bca4-4126c0eda2dd.pdf"},{"id":80273225,"identity":"1cc71cde-c0c5-467f-8cd3-795315729341","added_by":"auto","created_at":"2025-04-10 04:14:23","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1629636,"visible":true,"origin":"","legend":"","description":"","filename":"SciRptrevisedSupportingInfo202503281259final.docx","url":"https://assets-eu.researchsquare.com/files/rs-5999417/v1/73f2bbb75a9b392f174691d2.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Inverse Binary Optimization of Convolutional Neural Network in Active Learning Efficiently Designs Nanophotonic Structures","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Binary optimization, Active learning, Convolutional Neural Network, Inverse Optimization, Nanophotonics","lastPublishedDoi":"10.21203/rs.3.rs-5999417/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5999417/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBinary optimization using active learning schemes has gained attention for automating the discovery of optimal designs in nanophotonic structures and material configurations. Recently, active learning has utilized factorization machines (FM), which usually are second-order models, as surrogates to approximate the hypervolume of the design space, benefiting from rapid optimization by Ising machines such as quantum annealing (QA). However, due to their second-order nature, FM-based surrogate functions struggle to fully capture the complexity of the hypervolume. In this paper, we introduce an inverse binary optimization (IBO) scheme that optimizes a surrogate function based on a convolutional neural network (CNN) within an active learning framework. The IBO method employs backward error propagation to optimize the input binary vector, minimizing the output value while maintaining fixed parameters in the pre-trained CNN layers. We conduct a benchmarking study of the CNN-based surrogate function within the CNN-IBO framework by optimizing nanophotonic designs (e.g., planar multilayer and stratified grating structure) as a testbed. Our results demonstrate that CNN-IBO achieves optimal designs with fewer actively accumulated training data than FM-QA, indicating its potential as a powerful and efficient method for binary optimization.\u003c/p\u003e","manuscriptTitle":"Inverse Binary Optimization of Convolutional Neural Network in Active Learning Efficiently Designs Nanophotonic Structures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-10 03:58:18","doi":"10.21203/rs.3.rs-5999417/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-04-21T11:06:56+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-21T04:47:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-21T03:14:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"241211028881190807819709555172744362326","date":"2025-04-10T16:21:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"184990625876170984755882212402790919333","date":"2025-04-09T11:11:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"186857592098910921765298726199178578350","date":"2025-04-08T18:09:27+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-07T09:51:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-05T12:04:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-03-28T04:43:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4775dcf5-a15b-4201-955b-16b434560680","owner":[],"postedDate":"April 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46908736,"name":"Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics"},{"id":46908737,"name":"Physical sciences/Engineering/Electrical and electronic engineering"}],"tags":[],"updatedAt":"2025-05-05T16:02:47+00:00","versionOfRecord":{"articleIdentity":"rs-5999417","link":"https://doi.org/10.1038/s41598-025-99570-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-04-30 15:57:22","publishedOnDateReadable":"April 30th, 2025"},"versionCreatedAt":"2025-04-10 03:58:18","video":"","vorDoi":"10.1038/s41598-025-99570-z","vorDoiUrl":"https://doi.org/10.1038/s41598-025-99570-z","workflowStages":[]},"version":"v1","identity":"rs-5999417","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5999417","identity":"rs-5999417","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}