Observation-Guided Physics-Informed Neural Network (OG-PINN): Application to Subsurface Ocean Temperature and Salinity Structure Reconstruction

Observation-Guided Physics-Informed Neural Network (OG-PINN): Application to Subsurface Ocean Temperature and Salinity Structure Reconstruction | 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 Observation-Guided Physics-Informed Neural Network (OG-PINN): Application to Subsurface Ocean Temperature and Salinity Structure Reconstruction Yao Xiao, Youmin Tang, Yi Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8879567/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Marine observations are essential for climate forecasting, weather prediction, and Earth system dynamics research. However, due to cost and technological constraints, sub-surface ocean observations suffer from insufficient spatial coverage and poor temporal resolution. While data assimilation products provide three-dimensional fields, they often lag behind real-time requirements. To address this, we propose an Observation-Guided Physics-Informed Neural Network (OG-PINN), which efficiently reconstructs the three-dimensional temperature, salinity, and density structure of the ocean interior using surface observations. By embedding the seawater equation of state as a physical constraint within the network architecture, OG-PINN ensures thermodynamic consistency among temperature, salinity, and density. Crucially, by incorporating observational data into the physical loss, OG-PINN effectively resolves the optimization conflict between data and physical constraints inherent in standard Physics-Informed Neural Networks (PINNs). OG-PINN outperforms U-Net and standard PINNs in reconstructing subsurface temperature-salinity (T-S) structures by adaptively adjusting the weight of the physical loss function to balance data-fitting accuracy and physical constraint. Results demonstrate that OG-PINN reduces the root mean square error (RMSE) of tropical mean subsurface temperature anomalies (STA) and subsurface salinity anomalies (SSA) by up to 5%, while spatially averaged correlation coefficients between reconstructed fields and ground truth improve by up to 7% over standard PINNs. Notably, in dynamically complex upwelling regions, OG-PINN mitigates adverse effects from idealized physical constraints by dynamically reducing physical loss weight, whereas standard PINNs suffer from spurious convergence in physical losses, failing to achieve reasonable weight adjustment. This study not only validates the critical role of observation-guided physical constraints in enhancing both accuracy and physical consistency of sub-surface variable reconstruction, but also provides high-quality, timely initial fields for temperature and salinity to climate models. These advances hold significant scientific and practical implications for improving the predictability of key tropical climate modes such as El Niño-Southern Oscillation (ENSO). Deep-Learning Physics-Informed Neural Networks (PINN) Observation-Guided PINN Ocean Temperature and Salinity Reconstruction Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 19 Mar, 2026 Reviewers invited by journal 06 Mar, 2026 Editor assigned by journal 03 Mar, 2026 First submitted to journal 26 Feb, 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-8879567","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":601870675,"identity":"5208a0de-570f-4a06-9778-ff31fbec5c0d","order_by":0,"name":"Yao Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIie3RMQrCMBSA4ZZAujzsGq2oR2gpFAfxLJVAp7g7iDhlEme9RcELFILPRXDtJlJwcnByFFNHh7SjQ/4hhJAP8ojj2Gz/WrpgU58U9Zb125HnecK7Mv0SaCXcvczcHL/EaSbhSWEAVJEYCfbK5RgcTx1zIzlnPAZQnQQpjwXqh0GWlUZSiKgCpkhy3USVoJowSMzk8ggVhMo9SL2KdxtSiui2S/X4FKJqLluQbnnn4bOYcFbPMt8yoE2zdC4c2eytv1ISDMRrNfA9hUYyKn5PqOl63XDddMNms9lsH0ETRsBQUhbkAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-5136-6772","institution":"Hohai University","correspondingAuthor":true,"prefix":"","firstName":"Yao","middleName":"","lastName":"Xiao","suffix":""},{"id":601870676,"identity":"4ac59344-b32b-47bf-8164-10d9c0590486","order_by":1,"name":"Youmin Tang","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"Youmin","middleName":"","lastName":"Tang","suffix":""},{"id":601870677,"identity":"830cee33-4ef4-4593-af3f-3f45f7e081a7","order_by":2,"name":"Yi Li","email":"","orcid":"","institution":"Hohai University","correspondingAuthor":false,"prefix":"","firstName":"Yi","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2026-02-14 11:34:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8879567/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8879567/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104416200,"identity":"392e3aea-954d-426a-a082-475dafcf390c","added_by":"auto","created_at":"2026-03-11 13:14:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2322017,"visible":true,"origin":"","legend":"","description":"","filename":"OGPINNReconstructionmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8879567/v1_covered_7a88a1c7-7d00-4ffa-82a2-2ab9ebc366b4.pdf"}],"financialInterests":"","formattedTitle":"Observation-Guided Physics-Informed Neural Network (OG-PINN): Application to Subsurface Ocean Temperature and Salinity Structure Reconstruction","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"climate-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cldy","sideBox":"Learn more about [Climate Dynamics](https://www.springer.com/journal/382)","snPcode":"382","submissionUrl":"https://submission.nature.com/new-submission/382/3","title":"Climate Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Deep-Learning, Physics-Informed Neural Networks (PINN), Observation-Guided PINN, Ocean Temperature and Salinity Reconstruction","lastPublishedDoi":"10.21203/rs.3.rs-8879567/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8879567/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMarine observations are essential for climate forecasting, weather prediction, and Earth system dynamics research. However, due to cost and technological constraints, sub-surface ocean observations suffer from insufficient spatial coverage and poor temporal resolution. While data assimilation products provide three-dimensional fields, they often lag behind real-time requirements. To address this, we propose an Observation-Guided Physics-Informed Neural Network (OG-PINN), which efficiently reconstructs the three-dimensional temperature, salinity, and density structure of the ocean interior using surface observations. By embedding the seawater equation of state as a physical constraint within the network architecture, OG-PINN ensures thermodynamic consistency among temperature, salinity, and density. Crucially, by incorporating observational data into the physical loss, OG-PINN effectively resolves the optimization conflict between data and physical constraints inherent in standard Physics-Informed Neural Networks (PINNs).\u003c/p\u003e \u003cp\u003eOG-PINN outperforms U-Net and standard PINNs in reconstructing subsurface temperature-salinity (T-S) structures by adaptively adjusting the weight of the physical loss function to balance data-fitting accuracy and physical constraint. Results demonstrate that OG-PINN reduces the root mean square error (RMSE) of tropical mean subsurface temperature anomalies (STA) and subsurface salinity anomalies (SSA) by up to 5%, while spatially averaged correlation coefficients between reconstructed fields and ground truth improve by up to 7% over standard PINNs. Notably, in dynamically complex upwelling regions, OG-PINN mitigates adverse effects from idealized physical constraints by dynamically reducing physical loss weight, whereas standard PINNs suffer from spurious convergence in physical losses, failing to achieve reasonable weight adjustment. This study not only validates the critical role of observation-guided physical constraints in enhancing both accuracy and physical consistency of sub-surface variable reconstruction, but also provides high-quality, timely initial fields for temperature and salinity to climate models. These advances hold significant scientific and practical implications for improving the predictability of key tropical climate modes such as El Ni\u0026ntilde;o-Southern Oscillation (ENSO).\u003c/p\u003e","manuscriptTitle":"Observation-Guided Physics-Informed Neural Network (OG-PINN): Application to Subsurface Ocean Temperature and Salinity Structure Reconstruction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-11 12:27:05","doi":"10.21203/rs.3.rs-8879567/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-03-20T03:14:11+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-06T12:17:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-04T04:51:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Climate Dynamics","date":"2026-02-27T01:58:14+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"climate-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cldy","sideBox":"Learn more about [Climate Dynamics](https://www.springer.com/journal/382)","snPcode":"382","submissionUrl":"https://submission.nature.com/new-submission/382/3","title":"Climate Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"03262fe7-c3a3-4324-8603-ad677e486738","owner":[],"postedDate":"March 11th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-11T12:27:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-11 12:27:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8879567","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8879567","identity":"rs-8879567","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}