A physics-guided neural network with analytical self-attenuation correction for rapid efficiency calibration of HPGe detectors

A physics-guided neural network with analytical self-attenuation correction for rapid efficiency calibration of HPGe detectors | 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 A physics-guided neural network with analytical self-attenuation correction for rapid efficiency calibration of HPGe detectors Jonay González Guerra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9333166/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Efficiency calibration of HPGe detectors for environmental gamma-ray spectrometry requires knowing the full energy peak efficiency (FEPE) for each combination of photon energy, sample geometry and material composition. We present a physics-guided neural network that decouples this problem into a multilayer perceptron---trained on a single reference material to learn FEPE as a function of energy and sample height---and a fixed analytical layer that corrects for self-attenuation using XCOM mass attenuation coefficients. Two levels of geometric correction are evaluated: the classical parallel beam (PB) formula and a geometric ray-tracing (RT) approach with solid-angle weighting. The methodology is validated on two HPGe detectors of fundamentally different geometry---a well-type and a planar extended-range (XtRa) detector---using characterised PENELOPE Monte Carlo models as the data source. For each detector, the model is trained with IAEA-RGU-1 and tested against eight materials spanning densities from \SI{1.0}{\gram\per\centi\metre\cubed} (water) to \SI{2.7}{\gram\per\centi\metre\cubed} (ilmenite), at unseen energies and unseen sample heights. The solid-angle weighted RT correction is universally superior to the PB formula for both detector geometries, achieving a mean pipeline MAPE across all eight test materials of 3.0% ($R^2 = 0.994$) for the well-type detector and 1.8% ($R^2 = 0.999$) for the XtRa, compared to 4.1% and 2.3% with the PB formula. The pipeline MAPE remains below 5% for all materials on both detectors, including ilmenite ($\rho = \SI{2.7}{\gram\per\centi\metre\cubed}$). Once trained, the model yields FEPE predictions in under one second for any sample height and material, compared to tens to hundreds of seconds per Monte Carlo simulation, depending on sample size and the statistical precision required. Physical sciences/Materials science Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 18 May, 2026 Reviewers agreed at journal 11 May, 2026 Reviewers agreed at journal 07 May, 2026 Reviewers invited by journal 07 May, 2026 Editor assigned by journal 28 Apr, 2026 Editor invited by journal 28 Apr, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 27 Apr, 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-9333166","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":638059461,"identity":"d1ac82b9-600c-4fdb-9c5e-54795764ae8b","order_by":0,"name":"Jonay González Guerra","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYBACxgbmBiBlw8PG3nwAyJCQIUILI0hLmhw/z7EEkBYeouwBEoeNJWfkGIC4hLUw9y9sfPjjF3PihgM5n1/dqLHgYWA/fHQDXjtmPGw2kOxjA2o5u8065xjQYTxpaTfwaznYJmHYw5O44WDvNuMcNqAWCR4zQlrafyT2SCRuOMzzzDjnHzFa+hvbGA78MDCWbONhfpzbRpQtjM2SjQ0JwEBmM2PO7ZPgYSPkF8P+wwc//vjzn4dN/vHjzznf6uT42Q8fw69lRgLQqjYwm00CTOJTDgLy/AeA5B8wm/kDIdWjYBSMglEwMgEAmuBPhi4vG50AAAAASUVORK5CYII=","orcid":"","institution":"Universidad del Atlántico Medio","correspondingAuthor":true,"prefix":"","firstName":"Jonay","middleName":"González","lastName":"Guerra","suffix":""}],"badges":[],"createdAt":"2026-04-06 11:09:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9333166/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9333166/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109405386,"identity":"a2300a3e-d89f-495d-b8a6-0006c0fe180e","added_by":"auto","created_at":"2026-05-17 13:17:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2068845,"visible":true,"origin":"","legend":"","description":"","filename":"PaperANNFEPEsScientificReports27042026.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9333166/v1_covered_91aa234a-9f6d-461d-b5dc-d851480cd48f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A physics-guided neural network with analytical self-attenuation correction for rapid efficiency calibration of HPGe detectors","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":"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-9333166/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9333166/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Efficiency calibration of HPGe detectors for environmental gamma-ray spectrometry requires knowing the full energy peak efficiency (FEPE) for each combination of photon energy, sample geometry and material composition. We present a physics-guided neural network that decouples this problem into a multilayer perceptron---trained on a single reference material to learn FEPE as a function of energy and sample height---and a fixed analytical layer that corrects for self-attenuation using XCOM mass attenuation coefficients. Two levels of geometric correction are evaluated: the classical parallel beam (PB) formula and a geometric ray-tracing (RT) approach with solid-angle weighting. The methodology is validated on two HPGe detectors of fundamentally different geometry---a well-type and a planar extended-range (XtRa) detector---using characterised PENELOPE Monte Carlo models as the data source. For each detector, the model is trained with IAEA-RGU-1 and tested against eight materials spanning densities from \\SI{1.0}{\\gram\\per\\centi\\metre\\cubed} (water) to \\SI{2.7}{\\gram\\per\\centi\\metre\\cubed} (ilmenite), at unseen energies and unseen sample heights. The solid-angle weighted RT correction is universally superior to the PB formula for both detector geometries, achieving a mean pipeline MAPE across all eight test materials of 3.0\\% ($R^2 = 0.994$) for the well-type detector and 1.8\\% ($R^2 = 0.999$) for the XtRa, compared to 4.1\\% and 2.3\\% with the PB formula. The pipeline MAPE remains below 5\\% for all materials on both detectors, including ilmenite ($\\rho = \\SI{2.7}{\\gram\\per\\centi\\metre\\cubed}$). 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