Physics-Informed Neural Networks (PINN) for temporal forecasting of monsoon rainfall variability in southern peninsular India

Physics-Informed Neural Networks (PINN) for temporal forecasting of monsoon rainfall variability in southern peninsular India | 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 Physics-Informed Neural Networks (PINN) for temporal forecasting of monsoon rainfall variability in southern peninsular India Joseph Pious, Adityan S, Stanley Raj This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6185189/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 Rainfall significantly influences the climatic and hydrological systems of Southern Peninsular India, a region known for its intricate weather dynamics and reliance on monsoon rainfall. This study introduces a dual-methodology framework combining Exploratory Data Analysis (EDA) with a Physics-Informed Neural Network (PINN) to explore rainfall variability effectively. EDA is employed as an essential tool to derive insights from historical precipitation datasets through statistical analysis, enabling the identification of patterns, anomalies, and trends. To complement this statistical groundwork, a novel PINN model is developed, leveraging principles from Bernoulli's equation to enhance the learning process to forecast rainfall for five states of southern peninsula of India viz., Coastal Andra, Coastal Karnataka, Kerala, Tamil Nadu, Telangana. By mapping the loss gradient to pressure changes, momentum to kinetic energy, and regularization to potential energy, the PINN framework mirrors the principles of conservation and fluid dynamics, ensuring robust and efficient training convergence in neural networks. The model also incorporates innovative techniques, including a Convergence Weight Index (WCI) and adaptive weight updates guided by the rate of loss reduction, to improve training stability and prevent overfitting. Additionally, advancements in PINN methodologies, such as multi-task optimization, modular decomposition of large datasets, and integration with hybrid architectures, are utilized to address the challenges of noisy and nonlinear precipitation data. This study makes key contributions by providing a EDA and machine learning techniques, proposing a Bernoulli-inspired PINN for precipitation modeling, and introducing novel mechanisms to enhance predictive performance. The findings underscore the utility of physics-augmented machine learning models in analysing complex environmental systems like rainfall variability. Rainfall variability Extrapolaratory data analysis Physics Informed Neural Networks Sothern Peninsula Bernoulli approach Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Full Text Additional Declarations No competing interests reported. Table 1 is available in the Supplementary Files section. Supplementary Files Table1.docx GraphicalAbstract.png 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. 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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-6185189","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":475881503,"identity":"957d6b88-5901-4e46-90ce-629a10fd92e4","order_by":0,"name":"Joseph Pious","email":"","orcid":"","institution":"Loyola College","correspondingAuthor":false,"prefix":"","firstName":"Joseph","middleName":"","lastName":"Pious","suffix":""},{"id":475881504,"identity":"02f79f35-15b4-46c9-a386-90227ea9304f","order_by":1,"name":"Adityan S","email":"","orcid":"","institution":"Loyola 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Bernoulli approach","lastPublishedDoi":"10.21203/rs.3.rs-6185189/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6185189/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRainfall significantly influences the climatic and hydrological systems of Southern Peninsular India, a region known for its intricate weather dynamics and reliance on monsoon rainfall. This study introduces a dual-methodology framework combining Exploratory Data Analysis (EDA) with a Physics-Informed Neural Network (PINN) to explore rainfall variability effectively. EDA is employed as an essential tool to derive insights from historical precipitation datasets through statistical analysis, enabling the identification of patterns, anomalies, and trends. To complement this statistical groundwork, a novel PINN model is developed, leveraging principles from Bernoulli's equation to enhance the learning process to forecast rainfall for five states of southern peninsula of India viz., Coastal Andra, Coastal Karnataka, Kerala, Tamil Nadu, Telangana. By mapping the loss gradient to pressure changes, momentum to kinetic energy, and regularization to potential energy, the PINN framework mirrors the principles of conservation and fluid dynamics, ensuring robust and efficient training convergence in neural networks. The model also incorporates innovative techniques, including a Convergence Weight Index (WCI) and adaptive weight updates guided by the rate of loss reduction, to improve training stability and prevent overfitting. Additionally, advancements in PINN methodologies, such as multi-task optimization, modular decomposition of large datasets, and integration with hybrid architectures, are utilized to address the challenges of noisy and nonlinear precipitation data. This study makes key contributions by providing a EDA and machine learning techniques, proposing a Bernoulli-inspired PINN for precipitation modeling, and introducing novel mechanisms to enhance predictive performance. The findings underscore the utility of physics-augmented machine learning models in analysing complex environmental systems like rainfall variability.\u003c/p\u003e","manuscriptTitle":"Physics-Informed Neural Networks (PINN) for temporal forecasting of monsoon rainfall variability in southern peninsular India","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-25 09:01:57","doi":"10.21203/rs.3.rs-6185189/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":"1af440ac-9012-4b7e-aced-af5e9bdeff19","owner":[],"postedDate":"June 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-25T09:01:57+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-25 09:01:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6185189","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6185189","identity":"rs-6185189","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}