A Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting

A Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting | 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 A Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting Mohamed H. Mohamed This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8564234/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 Accurate long-term forecasting of cumulative oil production (Np) is essential for effective reservoir management, reserves estimation, and field development planning. However, traditional decline curve analysis (DCA) methods suffer from limited extrapolation capability, while purely traditional artificial intelligence (AI) models often produce physically inconsistent cumulative production trends when applied beyond the training period. In this study, a hybrid physics-constrained deep learning framework is proposed to improve long-term cumulative oil production forecasting. The developed approach integrates a deep neural network (DNN) with a physically motivated monotonicity constraint to enforce realistic cumulative production behavior during extrapolation. Furthermore, a multi-branch model (MBM) architecture is introduced to address the practical challenge of unavailable future input variables by independently predicting the required production parameters and supplying them to the main forecasting model, rather than relying on fixed or scenario-based assumptions. The proposed framework was evaluated using real production data from an Iraqi oil reservoir and benchmarked against conventional DCA methods, including exponential, harmonic, and hyperbolic models. The results demonstrate that the physics-constrained DNN significantly outperforms traditional approaches in long-term forecasting, achieving a symmetric mean absolute percentage error (sMAPE) of 4.38% and a coefficient of determination (R²) of 0.87 over the testing period. Unlike classical DCA and unconstrained AI models, the proposed method preserves stable and physically consistent cumulative production trends, particularly over extended extrapolation horizons. Overall, this study highlights the importance of incorporating physical constraints into AI-based production forecasting models and provides a robust and practical tool for long-term reservoir performance prediction. Petroleum Engineering Artificial Intelligence and Machine Learning Cumulative production forecasting Artificial intelligence Decline curve analysis Deep neural networks Physics-constrained Hybrid Physics model Full Text Additional Declarations The authors declare no competing interests. Supplementary Files GraphicalAbstract1.png Graphical abstract illustrating the proposed hybrid physics-constrained DNN framework for cumulative production forecasting. np.png NP : True VS AI model (before/after physics equation) mbmsystem.png Case-specific implementation of the MBM framework showing input features, predicted intermediate variables, and final output. 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. 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-8564234","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":572296134,"identity":"21bddd52-574f-4a84-b796-491805c93eb4","order_by":0,"name":"Mohamed H. 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04:14:10","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":55081,"visible":true,"origin":"","legend":"\u003cp\u003eGraphical abstract illustrating the proposed hybrid physics-constrained DNN framework for cumulative production forecasting.\u003c/p\u003e","description":"","filename":"GraphicalAbstract1.png","url":"https://assets-eu.researchsquare.com/files/rs-8564234/v1/10a0946ef37d0a03ea1dd147.png"},{"id":100364600,"identity":"373458aa-1a62-4b4a-ba53-86cf869b5149","added_by":"auto","created_at":"2026-01-16 07:53:59","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":73618,"visible":true,"origin":"","legend":"\u003cp\u003eNP : True VS AI model (before/after physics equation)\u003c/p\u003e","description":"","filename":"np.png","url":"https://assets-eu.researchsquare.com/files/rs-8564234/v1/74035a69f1b163773ad4f25f.png"},{"id":100103751,"identity":"f6af2d8e-3fd8-44f5-ad98-4567e1c9cc10","added_by":"auto","created_at":"2026-01-13 04:14:11","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":258288,"visible":true,"origin":"","legend":"\u003cp\u003eCase-specific implementation of the MBM framework showing input features, predicted intermediate variables, and final output.\u003c/p\u003e","description":"","filename":"mbmsystem.png","url":"https://assets-eu.researchsquare.com/files/rs-8564234/v1/e6ea01837cbfeca51e5737b3.png"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eA Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Technology- Iraq","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":"Cumulative production forecasting, Artificial intelligence, Decline curve analysis, Deep neural networks, Physics-constrained, Hybrid Physics model","lastPublishedDoi":"10.21203/rs.3.rs-8564234/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8564234/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate long-term forecasting of cumulative oil production (Np) is essential for effective reservoir management, reserves estimation, and field development planning. However, traditional decline curve analysis (DCA) methods suffer from limited extrapolation capability, while purely traditional artificial intelligence (AI) models often produce physically inconsistent cumulative production trends when applied beyond the training period.\u003c/p\u003e \u003cp\u003eIn this study, a hybrid physics-constrained deep learning framework is proposed to improve long-term cumulative oil production forecasting. The developed approach integrates a deep neural network (DNN) with a physically motivated monotonicity constraint to enforce realistic cumulative production behavior during extrapolation. Furthermore, a multi-branch model (MBM) architecture is introduced to address the practical challenge of unavailable future input variables by independently predicting the required production parameters and supplying them to the main forecasting model, rather than relying on fixed or scenario-based assumptions.\u003c/p\u003e \u003cp\u003eThe proposed framework was evaluated using real production data from an Iraqi oil reservoir and benchmarked against conventional DCA methods, including exponential, harmonic, and hyperbolic models. The results demonstrate that the physics-constrained DNN significantly outperforms traditional approaches in long-term forecasting, achieving a symmetric mean absolute percentage error (sMAPE) of 4.38% and a coefficient of determination (R\u0026sup2;) of 0.87 over the testing period. Unlike classical DCA and unconstrained AI models, the proposed method preserves stable and physically consistent cumulative production trends, particularly over extended extrapolation horizons.\u003c/p\u003e \u003cp\u003eOverall, this study highlights the importance of incorporating physical constraints into AI-based production forecasting models and provides a robust and practical tool for long-term reservoir performance prediction.\u003c/p\u003e","manuscriptTitle":"A Hybrid Physics-Constrained DNN Framework for Long-Term Cumulative Oil Production Forecasting","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-13 04:14:06","doi":"10.21203/rs.3.rs-8564234/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"dc28ca40-3b0f-4a07-b91b-77ce71df436f","owner":[],"postedDate":"January 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":60904277,"name":"Petroleum Engineering"},{"id":60904278,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2026-01-13T04:14:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-13 04:14:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8564234","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8564234","identity":"rs-8564234","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}