PhysEmbedFormer: A Physics-Guided Interpretable Architecture for Medium-Term Forecasting of PV Power

PhysEmbedFormer: A Physics-Guided Interpretable Architecture for Medium-Term Forecasting of PV Power | 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 PhysEmbedFormer: A Physics-Guided Interpretable Architecture for Medium-Term Forecasting of PV Power Yue Yu, Pavel Loskot, Yu Gao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7597739/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 14 You are reading this latest preprint version Abstract A day-ahead forecasting of photovoltaic (PV) power generation is crucial for the real-time balancing of renewable power grids. Such a forecasting is strongly dependent on the weather conditions, which makes the traditional forecasting methods ineffective. The physics-based forecasting models usually offer good interpretability, but limited accuracy. The attention-based models can achieve good performance, but they lack interpretability and robustness. The solution is to construct hybrid models, which provide the desired performance with at least some degree of interpretability. In this paper, an interpretable, physics-model guided architecture termed PhysEmbedFormer is proposed for forecasting the PV power data in the context of meteorological data. The interpretable forecasting is obtained by first decomposing the PV power samples into the physics-estimated component and the residual. The components are jointly embedded into the vector-space representations using a cross-modality module. The subsequent dual-stage Kolmogorov-Arnold Network (KAN) refinement module adjust the signals to improve the forecasting accuracy of simpler downstream forecasting models such as the previously proposed iTransformer. The extensive numerical experiments confirm that the proposed PhysEmbedFormer outperforms other competitive architectures for the forecasting horizons of up to 72 hours, while it is also more interpretable. Physical sciences/Energy science and technology Physical sciences/Engineering Physical sciences/Mathematics and computing Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementary.pdf Cite Share Download PDF Status: Published Journal Publication published 29 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 26 Nov, 2025 Reviews received at journal 22 Nov, 2025 Reviews received at journal 05 Nov, 2025 Reviews received at journal 30 Oct, 2025 Reviews received at journal 28 Oct, 2025 Reviewers agreed at journal 24 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers agreed at journal 23 Oct, 2025 Reviewers invited by journal 21 Oct, 2025 Editor assigned by journal 18 Sep, 2025 Editor invited by journal 18 Sep, 2025 Submission checks completed at journal 17 Sep, 2025 First submitted to journal 17 Sep, 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-7597739","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":537634996,"identity":"1f667c96-8f6b-4f4f-9d69-67200347ad5d","order_by":0,"name":"Yue Yu","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Yue","middleName":"","lastName":"Yu","suffix":""},{"id":537634997,"identity":"dd48dadc-6720-4c64-b826-6f719aec05e8","order_by":1,"name":"Pavel Loskot","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABE0lEQVRIie3RsUrEMBjA8a8U0iXQNYL2GSIdzuMO+ioJhXQ55MYODrmlLge3KvcijoFAXSKuHXsIN9dNQcSk6+UKboL5LyEhP5IQgFDor9avAQhA1DOASzu3A8TThFFH4pgyoPhXBNmTRgKTZJaY657RZXFxv2vrw9MXhlQdCdQLLpMX5SPz7SqnjAq+xxp13LhTlCBgKi7xLfMRqoQgjGqWkdKSxpJIChI1mkuCqZe8HqsPSwpH1iOJwZLvCdKVrX2+jvaWwEiQI/I8mT+8aeLe8rjVOeFNjhGG8oa1Vd7glZfMUr4ZhnpZkOfN4f2zybI0Nbwb7hZXu8T4L3ayggCz8TORb7+XACTqzOZQKBT6p/0Aj/JWGZzMIB0AAAAASUVORK5CYII=","orcid":"","institution":"Zhejiang University - University of Illinois Urbana-Champaign Institute, Zhejiang University","correspondingAuthor":true,"prefix":"","firstName":"Pavel","middleName":"","lastName":"Loskot","suffix":""},{"id":537634998,"identity":"608b344b-1f4b-44a0-b76f-16adc04447fa","order_by":2,"name":"Yu Gao","email":"","orcid":"","institution":"Midea Group (China)","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Gao","suffix":""}],"badges":[],"createdAt":"2025-09-12 07:38:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7597739/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7597739/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-34874-8","type":"published","date":"2026-01-29T15:59:29+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":94817184,"identity":"009d0288-30fe-4af2-86c2-60c18f479c09","added_by":"auto","created_at":"2025-10-31 05:03:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":246067,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7597739/v1/25185db48f14eb09292f8047.pdf"},{"id":94817183,"identity":"fcc1b518-98d1-4735-aa60-6285253defec","added_by":"auto","created_at":"2025-10-31 05:03:17","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5113,"visible":true,"origin":"","legend":"","description":"","filename":"d41d1a891e5b45fe849b9eda3645ba3c.json","url":"https://assets-eu.researchsquare.com/files/rs-7597739/v1/619961ffd6f36087ffa81646.json"},{"id":94817181,"identity":"ee142a01-6ff8-4b9d-a4e9-f2b8c5eab3dd","added_by":"auto","created_at":"2025-10-31 05:03:17","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":884300,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7597739/v1/0a05e7c470970450b22d1308.pdf"},{"id":101690828,"identity":"4ebb2368-5d6c-4c34-bd4d-d89dc2a73221","added_by":"auto","created_at":"2026-02-02 16:09:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":340221,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7597739/v1_covered_8c9451ca-3303-4c8f-807a-40bb82e8fbdf.pdf"},{"id":94817180,"identity":"823c1468-8e31-4f78-afaa-a294a8b89a91","added_by":"auto","created_at":"2025-10-31 05:03:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":884300,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7597739/v1/0c6e840ba3828fe6c42452f1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"PhysEmbedFormer: A Physics-Guided Interpretable Architecture for Medium-Term Forecasting of PV Power","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":"","lastPublishedDoi":"10.21203/rs.3.rs-7597739/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7597739/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A day-ahead forecasting of photovoltaic (PV) power generation is crucial for the real-time balancing of renewable power grids. Such a forecasting is strongly dependent on the weather conditions, which makes the traditional forecasting methods ineffective. The physics-based forecasting models usually offer good interpretability, but limited accuracy. The attention-based models can achieve good performance, but they lack interpretability and robustness. The solution is to construct hybrid models, which provide the desired performance with at least some degree of interpretability. In this paper, an interpretable, physics-model guided architecture termed PhysEmbedFormer is proposed for forecasting the PV power data in the context of meteorological data. The interpretable forecasting is obtained by first decomposing the PV power samples into the physics-estimated component and the residual. The components are jointly embedded into the vector-space representations using a cross-modality module. The subsequent dual-stage Kolmogorov-Arnold Network (KAN) refinement module adjust the signals to improve the forecasting accuracy of simpler downstream forecasting models such as the previously proposed iTransformer. The extensive numerical experiments confirm that the proposed PhysEmbedFormer outperforms other competitive architectures for the forecasting horizons of up to 72 hours, while it is also more interpretable.","manuscriptTitle":"PhysEmbedFormer: A Physics-Guided Interpretable Architecture for Medium-Term Forecasting of PV Power","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-31 05:03:12","doi":"10.21203/rs.3.rs-7597739/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-26T05:43:13+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-22T10:33:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-05T12:49:49+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-30T16:58:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-28T12:49:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"125408245021592727383870134366329893813","date":"2025-10-24T06:15:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"169265667625131500380764771605149304014","date":"2025-10-23T17:43:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"95170590690555251654486491504196794375","date":"2025-10-23T14:54:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"266031052401676066716866216552821721163","date":"2025-10-23T14:48:41+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-21T11:35:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-18T04:42:31+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-09-18T04:39:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-17T12:12:02+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-17T12:10:26+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":"ad586d24-7199-41b9-a1fc-5f6c3cd151eb","owner":[],"postedDate":"October 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":57178349,"name":"Physical sciences/Energy science and technology"},{"id":57178350,"name":"Physical sciences/Engineering"},{"id":57178351,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-02-02T16:05:54+00:00","versionOfRecord":{"articleIdentity":"rs-7597739","link":"https://doi.org/10.1038/s41598-025-34874-8","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-29 15:59:29","publishedOnDateReadable":"January 29th, 2026"},"versionCreatedAt":"2025-10-31 05:03:12","video":"","vorDoi":"10.1038/s41598-025-34874-8","vorDoiUrl":"https://doi.org/10.1038/s41598-025-34874-8","workflowStages":[]},"version":"v1","identity":"rs-7597739","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7597739","identity":"rs-7597739","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}