Bgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery | 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 Bgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery Bin Cao, Jie Xiong, Jiaxuan Ma, Yuan Tian, Yirui Hu, Mengwei He, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8665853/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract Efficient exploration of vast compositional and processing spaces is essential for accelerated materials discovery. Bayesian optimization (BO) provides a principled strategy for identifying optimal materials with minimal experiments, yet its adoption in materials science ishindered by implementation complexity and limited domain-specific tools. Here, we presentBgolearn, a comprehensive Python framework that makes BO accessible and practical for materials research through an intuitive interface, robust algorithms, and materials-oriented workflows. Bgolearn supports both single-objective and multi-objective Bayesian optimization withmultiple acquisition functions (e.g., expected improvement, upper confidence bound, probability of improvement, and expected hypervolume improvement etc.), diverse surrogate models(including Gaussian processes, random forests, and gradient boosting etc.), and bootstrapbased uncertainty quantification. Benchmark studies show that Bgolearn reduces the numberof required experiments by 40–60% compared with random search, grid search, and geneticalgorithms, while maintaining comparable or superior solution quality. Its effectiveness isdemonstrated not only through the studies presented in this paper, such as the identificationof maximum-elastic-modulus triply periodic minimal surface structures, ultra-high-hardnesshigh-entropy alloys, and high-strength, high-ductility medium-Mn steels, but also by numerous publications that have proven its impact in material discovery. With a modular architecture that integrates seamlessly into existing materials workflows and a graphical user interface (BgoFace) that removes programming barriers, Bgolearn establishes a practical andreliable platform for Bayesian optimization in materials science, and is openly available at https://github.com/Bin-Cao/Bgolearn . Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Bayesian optimization Bgolearn Multi-objective Modular architecture Materials discovery Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Apr, 2026 Reviews received at journal 12 Apr, 2026 Reviews received at journal 10 Apr, 2026 Reviews received at journal 06 Apr, 2026 Reviews received at journal 02 Apr, 2026 Reviewers agreed at journal 16 Mar, 2026 Reviewers agreed at journal 16 Mar, 2026 Reviewers agreed at journal 14 Mar, 2026 Reviewers agreed at journal 11 Mar, 2026 Reviewers invited by journal 11 Mar, 2026 Editor assigned by journal 29 Jan, 2026 Submission checks completed at journal 28 Jan, 2026 First submitted to journal 22 Jan, 2026 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-8665853","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":582262312,"identity":"9a0e2eb3-470c-484a-bcf1-08ae9fb4d3a9","order_by":0,"name":"Bin Cao","email":"","orcid":"","institution":"The Hong Kong University of Science and Technology (Guangzhou)","correspondingAuthor":false,"prefix":"","firstName":"Bin","middleName":"","lastName":"Cao","suffix":""},{"id":582262313,"identity":"b8d9382b-a8a3-43bf-bc41-6a5f068df328","order_by":1,"name":"Jie Xiong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYDACZhDBI8HAz8AD5xKpRbKBaC0wYHCAWC0Gx5mPPfwiYyFnfP7sMQmGCuvEBvazB/BqkWxmSzeW4ZEwNruRlybBcCY9sYEnLwGvFn5mHjNpCR6JxG03eMwkGNsOJzZI8Bjg1cIG1VK/uf8MUMs/IrSAbJH8wCORYMCQA9TSQIQWoF/SpIGBbDjjRo6xRcKxdOM2nhz8WgzOHz4m+bOnTp6//4zhjQ811rL97GfwawEBZt4eKCsB5DuC6oGA8ccPYpSNglEwCkbBiAUAFIg33s01nDEAAAAASUVORK5CYII=","orcid":"","institution":"Shanghai University","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Xiong","suffix":""},{"id":582262318,"identity":"92a9a934-2cca-43b5-ba66-89985baad178","order_by":2,"name":"Jiaxuan Ma","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Jiaxuan","middleName":"","lastName":"Ma","suffix":""},{"id":582262319,"identity":"e3c01a49-948d-444b-977c-4ff278bac064","order_by":3,"name":"Yuan Tian","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Yuan","middleName":"","lastName":"Tian","suffix":""},{"id":582262320,"identity":"a2aa1323-bdb7-4fcb-a106-d1f8d6a415e5","order_by":4,"name":"Yirui Hu","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Yirui","middleName":"","lastName":"Hu","suffix":""},{"id":582262337,"identity":"d087a024-a3c0-4f8d-91b0-a4463bac13ca","order_by":5,"name":"Mengwei He","email":"","orcid":"","institution":"The University of Sydney","correspondingAuthor":false,"prefix":"","firstName":"Mengwei","middleName":"","lastName":"He","suffix":""},{"id":582262338,"identity":"bf811b4e-ceec-43cb-a9b9-b3e388b9522c","order_by":6,"name":"Longhan Zhang","email":"","orcid":"","institution":"The Hong Kong University of Science and Technology (Guangzhou)","correspondingAuthor":false,"prefix":"","firstName":"Longhan","middleName":"","lastName":"Zhang","suffix":""},{"id":582262339,"identity":"3766498b-dcce-4631-8fc2-81b5f68d5f6f","order_by":7,"name":"Jiayu Wang","email":"","orcid":"","institution":"Harbin Institute of Technology (Shenzhen)","correspondingAuthor":false,"prefix":"","firstName":"Jiayu","middleName":"","lastName":"Wang","suffix":""},{"id":582262340,"identity":"f5cab25c-e482-4629-96aa-2a2572f91c7a","order_by":8,"name":"Jian Hui","email":"","orcid":"","institution":"Suzhou Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Jian","middleName":"","lastName":"Hui","suffix":""},{"id":582262341,"identity":"cbc6990d-eb7d-4e10-bf5f-4af7b7543be5","order_by":9,"name":"Li Liu","email":"","orcid":"","institution":"Harbin Institute of Technology (Shenzhen)","correspondingAuthor":false,"prefix":"","firstName":"Li","middleName":"","lastName":"Liu","suffix":""},{"id":582262342,"identity":"078e5c75-8698-466c-8859-0e4ff9368414","order_by":10,"name":"Dezhen Xue","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Dezhen","middleName":"","lastName":"Xue","suffix":""},{"id":582262343,"identity":"adaf1fed-c8fe-47c8-8d5c-2ba4d7d22540","order_by":11,"name":"Turab Lookman","email":"","orcid":"","institution":"AiMaterials Research","correspondingAuthor":false,"prefix":"","firstName":"Turab","middleName":"","lastName":"Lookman","suffix":""},{"id":582262344,"identity":"eaad110c-2210-45b9-a7c8-7ee70c3b6ece","order_by":12,"name":"Tong-Yi Zhang","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Tong-Yi","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-01-22 06:11:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8665853/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8665853/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103507439,"identity":"f3c885c6-336f-49d8-9a10-078912aecb91","added_by":"auto","created_at":"2026-02-26 13:41:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3919981,"visible":true,"origin":"","legend":"","description":"","filename":"Bgolearn.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8665853/v1_covered_79d503d8-7d4c-43c6-910a-31b48041c527.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eBgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"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":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Bayesian optimization, Bgolearn, Multi-objective, Modular architecture, Materials discovery","lastPublishedDoi":"10.21203/rs.3.rs-8665853/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8665853/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Efficient exploration of vast compositional and processing spaces is essential for acceler\u0002ated materials discovery. Bayesian optimization (BO) provides a principled strategy for iden\u0002tifying optimal materials with minimal experiments, yet its adoption in materials science ishindered by implementation complexity and limited domain-specific tools. Here, we presentBgolearn, a comprehensive Python framework that makes BO accessible and practical for ma\u0002terials research through an intuitive interface, robust algorithms, and materials-oriented work\u0002flows. Bgolearn supports both single-objective and multi-objective Bayesian optimization withmultiple acquisition functions (e.g., expected improvement, upper confidence bound, probabil\u0002ity of improvement, and expected hypervolume improvement etc.), diverse surrogate models(including Gaussian processes, random forests, and gradient boosting etc.), and bootstrap\u0002based uncertainty quantification. Benchmark studies show that Bgolearn reduces the numberof required experiments by 40–60% compared with random search, grid search, and geneticalgorithms, while maintaining comparable or superior solution quality. Its effectiveness isdemonstrated not only through the studies presented in this paper, such as the identificationof maximum-elastic-modulus triply periodic minimal surface structures, ultra-high-hardnesshigh-entropy alloys, and high-strength, high-ductility medium-Mn steels, but also by numer\u0002ous publications that have proven its impact in material discovery. With a modular archi\u0002tecture that integrates seamlessly into existing materials workflows and a graphical user in\u0002terface (BgoFace) that removes programming barriers, Bgolearn establishes a practical andreliable platform for Bayesian optimization in materials science, and is openly available athttps://github.com/Bin-Cao/Bgolearn.","manuscriptTitle":"Bgolearn: a Unified Bayesian Optimization Framework for Accelerating Materials Discovery","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-25 09:06:13","doi":"10.21203/rs.3.rs-8665853/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-28T10:58:33+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-13T01:57:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-11T00:10:26+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-06T19:56:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-02T22:18:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"179333588119979517298727931305496526192","date":"2026-03-16T14:51:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"208174365086833183533658192515205441710","date":"2026-03-16T11:56:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240764866290874938460974274763312562845","date":"2026-03-14T14:44:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"213974332196645067060110340988417280165","date":"2026-03-11T14:15:34+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-11T11:40:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-29T07:39:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-28T05:06:11+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Computational Materials","date":"2026-01-22T06:00:52+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"
[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"592876bc-cb67-4e89-a77e-ca816f59eca5","owner":[],"postedDate":"February 25th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":63498891,"name":"Physical sciences/Engineering"},{"id":63498892,"name":"Physical sciences/Materials science"},{"id":63498893,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-12T15:23:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-25 09:06:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8665853","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8665853","identity":"rs-8665853","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}
Text is read by the "Ask this paper" AI Q&A widget below.
Extraction quality varies by source — PMC NXML preserves structure
cleanly, OA-HTML may include some navigation residue, and OA-PDF can
have broken hyphenation. The publisher copy
(via DOI)
is the canonical version.