Transfer learning electronic structure: millielectron-volt accuracy for sub-million-atom moiré semiconductor

Transfer learning electronic structure: millielectron-volt accuracy for sub-million-atom moiré semiconductor | 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 Brief Communication Transfer learning electronic structure: millielectron-volt accuracy for sub-million-atom moiré semiconductor Yang Zhang, Ting Bao, Ning Mao, Wenhui Duan, Yong Xu, Adrian Del Maestro This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5920488/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 The integration of density functional theory (DFT) with machine learning enables efficient ab initio electronic structure calculations for ultra-large systems. In this work, we develop a transfer learning framework tailored for long-wavelength moir ́e systems. To balance efficiency and accuracy, we adopt a two-step transfer learning strategy: (1) the model is pre-trained on a large dataset of computationally inexpensive non-twisted structures until convergence, and (2) the network is then fine-tuned using a small set of computationally expensive twisted structures. Applying this method to twisted MoTe2, the neural network model generates the resulting Hamiltonian for a 1000-atom system in 200 seconds, achieving a mean absolute error below 0.1 meV. To demonstrate O(N) scalability, we model nanoribbon systems with up to 0.25 million atoms (∼ 9 million orbitals), accu- rately capturing edge states consistent with predicted Chern numbers. This approach addresses the challenges of accuracy, efficiency, and scalability, offering a viable alternative to conventional DFT and enabling the exploration of electronic topology in large scale moir ́e systems towards simulating realistic device architectures. Physical sciences/Materials science/Theory and computation/Electronic structure Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological insulators Full Text Additional Declarations There is NO Competing Interest. 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. 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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-5920488","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Brief Communication","associatedPublications":[],"authors":[{"id":418732781,"identity":"58ae874c-f34c-4698-9d73-e3733cfb2a3b","order_by":0,"name":"Yang Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYLACxgYgwd4ApsFsIrXwHGBsJFGLRAKRWgyOnz388ucOuzz5yDfmD2cw2MhuOEBIy5m8NAvJM8nFhrdzDBs3MKQZE9ZyIMfMwLCNOXHjbKCWBwyHEwlrOf/GzCCxrT5x48wzIC3/idByI8f4wcG2w4nzJXhADjtAWIvkjTdmjI1txxM38KQVzpxhkGw8k5AWvvM5xh9/tlUnzm8/vOFjT4WdbB8hLQoHGNgkwC4EqzQgoBwE5BsYmD9AGaNgFIyCUTAKsAMApLpQDs+uNoMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0003-4630-5056","institution":"University of Tennessee","correspondingAuthor":true,"prefix":"","firstName":"Yang","middleName":"","lastName":"Zhang","suffix":""},{"id":418732782,"identity":"da64a33e-01a3-46ac-8a8e-d23988e1fcf1","order_by":1,"name":"Ting Bao","email":"","orcid":"","institution":"University of Tennessee","correspondingAuthor":false,"prefix":"","firstName":"Ting","middleName":"","lastName":"Bao","suffix":""},{"id":418732783,"identity":"5d02a3b2-78c9-4919-84e9-02c7d0a17e82","order_by":2,"name":"Ning Mao","email":"","orcid":"","institution":"Max Planck Institute Chemical Physics of Solids","correspondingAuthor":false,"prefix":"","firstName":"Ning","middleName":"","lastName":"Mao","suffix":""},{"id":418732784,"identity":"61ccf39e-1e57-449e-9bf3-30a95c6fbfac","order_by":3,"name":"Wenhui Duan","email":"","orcid":"https://orcid.org/0000-0001-9685-2547","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Wenhui","middleName":"","lastName":"Duan","suffix":""},{"id":418732785,"identity":"5d8f980f-3549-412f-8a42-2c06680ef704","order_by":4,"name":"Yong Xu","email":"","orcid":"https://orcid.org/0000-0002-4844-2460","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Yong","middleName":"","lastName":"Xu","suffix":""},{"id":418732786,"identity":"cf2aff3d-fd2b-4c76-86ae-cf6edd8c3f7e","order_by":5,"name":"Adrian Del Maestro","email":"","orcid":"","institution":"University of Tennessee Knoxville","correspondingAuthor":false,"prefix":"","firstName":"Adrian","middleName":"Del","lastName":"Maestro","suffix":""}],"badges":[],"createdAt":"2025-01-28 19:07:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5920488/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5920488/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94729378,"identity":"fb1d5ae6-f270-4dfb-bbc3-ad318f113c72","added_by":"auto","created_at":"2025-10-30 07:04:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8273473,"visible":true,"origin":"","legend":"Article File","description":"","filename":"NATCOMPUTSCI250289ManuTransferlearning.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5920488/v1_covered_4a0088d3-6c0b-48bf-9a8e-c248a71c4e07.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eTransfer learning electronic structure: millielectron-volt accuracy for sub-million-atom moiré semiconductor\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":"","lastPublishedDoi":"10.21203/rs.3.rs-5920488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5920488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The integration of density functional theory (DFT) with machine learning enables efficient ab initio electronic structure calculations for ultra-large systems. 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