Parameter Estimation of 3D-GTD Model Based on a Multi-Neural Network

Parameter Estimation of 3D-GTD Model Based on a Multi-Neural Network | 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 Parameter Estimation of 3D-GTD Model Based on a Multi-Neural Network Mingrui Qi, Lihua Wu, Rui Cao, Minghao Peng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8209921/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract In this article, a novel parameter estimation method of three-dimensional geometrical theory of diffraction(3D-GTD) model based on a multi-neural network is proposed. By leveraging multi-view one-dimensional geometrical theory of diffraction(1D-GTD) parameters as input, the three-branch neural network simultaneously estimates 3D scattering center parameters—position, intensity, and type. Position reconstruction branch employs geometric encoding and gated fusion for joint feature extraction, combined with hierarchical attention and coordinate regression. Scattering intensity estimation branch achieves efficient feature aggregation via multi-level convolutional layers and parameter sharing mechanism, enabling high-precision intensity parameter estimation while ensuring model lightweight. Type identification branch establishes a mapping from numerical features to categorical indices, which converts the regression task into a classification task that conforms to discrete value constraints. It employs a sub-channel processing architecture and a shared multi-layer perceptron (MLP) to effectively aggregate multi-view predictive information, thereby achieving accurate identification of scattering center types. To address the challenge of difficult acquisition of training data, we construct a self-generated dataset with random characteristics, thereby enhancing the generalization performance of the network. Experimental results show the proposed method outperforms traditional approaches in estimation accuracy across different signal-to-noise ratio (SNR) levels and computational efficiency. Physical sciences/Engineering Physical sciences/Mathematics and computing Three-dimensional geometrical theory of diffraction(3D-GTD) model multi-neural network scattering center parameters self-generated dataset Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 22 Dec, 2025 Reviews received at journal 19 Dec, 2025 Reviews received at journal 17 Dec, 2025 Reviewers agreed at journal 16 Dec, 2025 Reviewers agreed at journal 16 Dec, 2025 Reviewers agreed at journal 14 Dec, 2025 Reviewers invited by journal 04 Dec, 2025 Editor invited by journal 01 Dec, 2025 Editor assigned by journal 27 Nov, 2025 Submission checks completed at journal 27 Nov, 2025 First submitted to journal 26 Nov, 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-8209921","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":556279304,"identity":"3ec1d361-422e-4bb6-af1c-db45e938c606","order_by":0,"name":"Mingrui Qi","email":"","orcid":"","institution":"Northwest Institute of Nuclear Technology","correspondingAuthor":false,"prefix":"","firstName":"Mingrui","middleName":"","lastName":"Qi","suffix":""},{"id":556279305,"identity":"90ebeb48-144b-4c61-a374-6081174d430c","order_by":1,"name":"Lihua Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYFAC5obDQFKOgR3EMQARCUDMhk8LI1iLMQMzXEsyYS0gxYlgEgIIaDG4kdh4uLDNLr2/mcd0c0EBQ57B8fwDDB/KDjPwz27ApaXh8My25NwZh3nMbs8wYCg2OPOYgXHGucMMEncOYNViBtLC28ac2wDSwmPAkLjhRjIDM2/bYQYDiQR8WurT5VG0/CWs5XCCAYoWRjxa7M88BDrp3HHDjYfZyoBaJBJnnnlscLDnXDqPxA3sWiTbkw9/5imrlpc73rztNs8fm8S+44kPH/wos5bjn4FdCzqQAJMHgJiHKPWjYBSMglEwCrACADqSYLCese24AAAAAElFTkSuQmCC","orcid":"","institution":"Northwest Institute of Nuclear Technology","correspondingAuthor":true,"prefix":"","firstName":"Lihua","middleName":"","lastName":"Wu","suffix":""},{"id":556279306,"identity":"54b8e6b9-ef9f-4c87-a049-ff0c354bac8a","order_by":2,"name":"Rui Cao","email":"","orcid":"","institution":"Northwest Institute of Nuclear Technology","correspondingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"Cao","suffix":""},{"id":556279307,"identity":"8cb22c6c-9cb1-483b-bde4-9094f4bda84d","order_by":3,"name":"Minghao Peng","email":"","orcid":"","institution":"Northwest Institute of Nuclear Technology","correspondingAuthor":false,"prefix":"","firstName":"Minghao","middleName":"","lastName":"Peng","suffix":""}],"badges":[],"createdAt":"2025-11-26 07:38:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8209921/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8209921/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97643257,"identity":"1413645b-1054-4286-9d2d-48e066cccbf3","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1046981,"visible":true,"origin":"","legend":"","description":"","filename":"ParameterEstimationof3DGTDModelBasedonaMultiNeuralNetwork.docx","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/d51dd30b1bd91ce6d0235b6f.docx"},{"id":97643258,"identity":"b6bf7f8e-4549-4f53-8981-ce8ccc0f3e00","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":974771,"visible":true,"origin":"","legend":"","description":"","filename":"Figures.docx","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/5ea1534978dcd1e0296ab0c6.docx"},{"id":97643250,"identity":"c8ffd948-5740-47dc-8c12-8248a731b7e8","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":30747,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/ccd161aadd7682a765e0bb05.docx"},{"id":97643252,"identity":"10207fa8-401a-4d3b-ac81-c73c8df11af4","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"json","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5978,"visible":true,"origin":"","legend":"","description":"","filename":"ba047de5978c44d0b8088d7b5955ea02.json","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/29e71b5847063f5f19834763.json"},{"id":97673979,"identity":"7a86fcb7-9fc8-4898-a0ca-3eabcf308223","added_by":"auto","created_at":"2025-12-08 09:42:02","extension":"xml","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":138928,"visible":true,"origin":"","legend":"","description":"","filename":"ba047de5978c44d0b8088d7b5955ea021enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/65611d18e90221374cec700d.xml"},{"id":97674511,"identity":"33f339e3-28b1-45ad-b590-7a8e5cf0f14b","added_by":"auto","created_at":"2025-12-08 09:43:30","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77326,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/a3141e2cf979448ed904e880.png"},{"id":97673804,"identity":"7c022126-fe7f-4b66-b368-6b9165df76cc","added_by":"auto","created_at":"2025-12-08 09:41:27","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27813,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/ebe7d73e8628867eb765930a.png"},{"id":97673871,"identity":"161a7ef2-50e3-471d-825b-4d9cd0064eb7","added_by":"auto","created_at":"2025-12-08 09:41:42","extension":"jpeg","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":599328,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/f47a6350f28e3973121e62b0.jpeg"},{"id":97643259,"identity":"dd604c71-f46e-4785-a6fc-5b41ff4ef0c2","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77326,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/6d46b54fbc5cbf085d2a3ce3.png"},{"id":97673570,"identity":"259d67e3-d23f-47df-a557-421110582f1e","added_by":"auto","created_at":"2025-12-08 09:40:39","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":99325,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/f69a666a1531bc11d4a681fa.png"},{"id":97643262,"identity":"31c8027b-ae98-4bda-9d39-a855946616bb","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":75114,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/951224ede71482036bd500bb.png"},{"id":97673264,"identity":"b9b65cb9-d985-4cc4-a67c-4114edcea328","added_by":"auto","created_at":"2025-12-08 09:39:46","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77177,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/f6b4330d18f2b636e7c97656.png"},{"id":97643268,"identity":"742169e9-2f60-446f-aa6e-e3d444a26f64","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104140,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/d56a0d1537212b23dc7cf7a4.png"},{"id":97674111,"identity":"8ff1cd0d-29eb-4b20-8214-51c32ff443b2","added_by":"auto","created_at":"2025-12-08 09:42:25","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63613,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/b730d928a6544b7bad8b4375.jpeg"},{"id":97643292,"identity":"d00818f8-c4f7-428f-b216-69f5c86f3bca","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"jpeg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":282884,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage18.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/8c7c94bcd8536f030a22ceb0.jpeg"},{"id":97674110,"identity":"7d290547-e853-4360-987e-859374f41b4d","added_by":"auto","created_at":"2025-12-08 09:42:25","extension":"jpeg","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":508851,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage19.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/f730c1fd42909ce2e7ada6fa.jpeg"},{"id":97643284,"identity":"4c83458e-b01d-482b-ad45-24fd00880474","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":99325,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/28b5b1041ee681d5d3172c83.png"},{"id":97643270,"identity":"9d68d8be-631d-442c-b929-4ed0f9815d6c","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33228,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/33ec5e68fb2f5345afa8ac40.png"},{"id":97643264,"identity":"efa7e3e1-bd6e-43cd-8513-580995cbf1f0","added_by":"auto","created_at":"2025-12-08 03:57:54","extension":"png","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27813,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/7e12e49b40fc1be0875203eb.png"},{"id":97643272,"identity":"19c39b13-7328-48fa-b222-186d229ea273","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"jpeg","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":599328,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/4a05d3b0a759b7654af468db.jpeg"},{"id":97673493,"identity":"329147cc-0bb3-4c83-95f9-1ff8b7bc9d1c","added_by":"auto","created_at":"2025-12-08 09:40:24","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":75114,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/d4c6e53de92cf88b04627c15.png"},{"id":97673763,"identity":"b594f2de-cd08-4380-9745-0ca7cadf77ae","added_by":"auto","created_at":"2025-12-08 09:41:21","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77177,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/dc6bdd935a30055b9a4d96f6.png"},{"id":97673587,"identity":"bd63b4c1-aebe-4694-8209-cff29706236b","added_by":"auto","created_at":"2025-12-08 09:40:42","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":104140,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/3f2d5fc6b425ce06e7c25517.png"},{"id":97673911,"identity":"d99fca07-d682-4d97-98f9-845aafb253bd","added_by":"auto","created_at":"2025-12-08 09:41:52","extension":"jpeg","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63613,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/26595b86893f1e7a09d3601c.jpeg"},{"id":97673924,"identity":"7c504fd3-e80f-4309-88ea-cb8be5d78738","added_by":"auto","created_at":"2025-12-08 09:41:54","extension":"jpeg","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":282884,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage18.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/84009c8db4efe1b13ed85aeb.jpeg"},{"id":97643293,"identity":"fbd14699-fdef-4766-8fb7-c4b135839323","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"jpeg","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":508851,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage19.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/2c3a29cea063b857098e0660.jpeg"},{"id":97643286,"identity":"cd2f6a54-8778-4d6f-a612-2bf2d637b4e7","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":33228,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/377ca1c563489601186280e6.png"},{"id":97674300,"identity":"94b675b8-f1e1-4061-917d-ea423e17339f","added_by":"auto","created_at":"2025-12-08 09:42:56","extension":"wmf","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image121.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/f3e01d72e9606e6f922c56d2.wmf"},{"id":97673943,"identity":"d62be625-9c17-4b40-bac2-5cff08e2c23b","added_by":"auto","created_at":"2025-12-08 09:41:57","extension":"wmf","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image2.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/b5c027153e713a96095fcd00.wmf"},{"id":97673453,"identity":"1af7ae37-bb55-495e-82e0-6a2e5a6768a0","added_by":"auto","created_at":"2025-12-08 09:40:19","extension":"wmf","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image72.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/c1ee37df3d4785f982da919c.wmf"},{"id":97643289,"identity":"90d0f3e1-3260-47f1-9611-bd1fedbd7fa4","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"wmf","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image73.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/51cc3dc2bbff13548213ab9a.wmf"},{"id":97673913,"identity":"ac5a8a1d-92e5-43e7-b3a6-4995944b8462","added_by":"auto","created_at":"2025-12-08 09:41:52","extension":"wmf","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image74.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/cf6ecb0f8214368d3044fc5b.wmf"},{"id":97643287,"identity":"bf679340-69de-42a2-aaf7-75c5ca4904bb","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"wmf","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image75.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/738484be49ddfb24a24f7124.wmf"},{"id":97643303,"identity":"a06e4cd9-a865-4c54-bbde-9618acfa1f3f","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"wmf","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":624,"visible":true,"origin":"","legend":"","description":"","filename":"image90.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/24a215556c922b445dbe83a0.wmf"},{"id":97673734,"identity":"c2640604-4efc-46de-b7db-a7a48f1c6478","added_by":"auto","created_at":"2025-12-08 09:41:12","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":25861,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/28a528d539fa8d9b9303da57.png"},{"id":97674274,"identity":"b39fb2a3-436d-4bd3-8d91-601b66a8c202","added_by":"auto","created_at":"2025-12-08 09:42:52","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10727,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/d6db85249c0e8daf6ace980a.png"},{"id":97643281,"identity":"6931b714-3a1b-42cf-a8fc-5f28aa57a724","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":179330,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/63646dfcdc7f241374443d0f.png"},{"id":97643278,"identity":"08fadcf4-a46d-4d02-8ed3-fcd03d0a1852","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":25861,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/1b2bda015e5840cd358c09e4.png"},{"id":97674191,"identity":"4b254484-13cc-4920-8432-b245d7ff519c","added_by":"auto","created_at":"2025-12-08 09:42:36","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":16557,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/b5b75f0d84755de5d18de888.png"},{"id":97674216,"identity":"812248d2-4ac4-4170-9d1f-fcfc98d9b1f1","added_by":"auto","created_at":"2025-12-08 09:42:38","extension":"png","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29081,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/a29bffb7278a2d08c3bec880.png"},{"id":97674097,"identity":"c1a49157-e651-4045-8d85-44dc631d0035","added_by":"auto","created_at":"2025-12-08 09:42:25","extension":"png","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23994,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/a7475c87b5ea6bc7071a1a36.png"},{"id":97673873,"identity":"8c178eee-bf45-4a6e-b41b-528ff255f1f6","added_by":"auto","created_at":"2025-12-08 09:41:43","extension":"png","order_by":41,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37987,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/5d4e74be2c22040a625fef97.png"},{"id":97673631,"identity":"f924c38f-8ad9-4c75-81cd-df81ccec6b9f","added_by":"auto","created_at":"2025-12-08 09:40:52","extension":"png","order_by":42,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11419,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/ee8a7b919c486a870ff703b0.png"},{"id":97673440,"identity":"6d6abec6-b212-4571-8bdb-bf11bf151558","added_by":"auto","created_at":"2025-12-08 09:40:15","extension":"png","order_by":43,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59418,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/05304810d685274f3b98618a.png"},{"id":97674467,"identity":"df50142b-d5cf-471b-b8fe-bf424982990a","added_by":"auto","created_at":"2025-12-08 09:43:22","extension":"png","order_by":44,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":97563,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/38ca59bb748a13d7cb856141.png"},{"id":97674138,"identity":"7a8382cd-e8b9-4006-9275-63324492728e","added_by":"auto","created_at":"2025-12-08 09:42:28","extension":"png","order_by":45,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":16557,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/037164c60cb7f24be45a918b.png"},{"id":97643274,"identity":"df1dad82-097e-4f01-9c13-f0f504583cf7","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":46,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13719,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/4b2b0bfe49d244ab67ac6f92.png"},{"id":97643311,"identity":"75ed6f94-9dfe-4d3c-b39f-6e6d7ecc04f4","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"png","order_by":47,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10727,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/eafa1c942b415f33d68c81c9.png"},{"id":97673951,"identity":"2ff9673c-6f0b-4579-ad06-3b28330598c6","added_by":"auto","created_at":"2025-12-08 09:41:59","extension":"png","order_by":48,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":179330,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage22.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/4a7d49c158566ba667ef81b6.png"},{"id":97674264,"identity":"cc6634c6-aa1b-4b55-b6fc-8a801b91dc3d","added_by":"auto","created_at":"2025-12-08 09:42:51","extension":"png","order_by":49,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29081,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/72492f32d49d35d130c254d3.png"},{"id":97643294,"identity":"02806f7e-ac25-4f0b-a97a-6ecc5947cdd2","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":50,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23994,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/8e4e83dc59bf394c0aa43d27.png"},{"id":97643295,"identity":"c68719f5-deb4-4a99-ab01-835583425d7c","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":51,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37987,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/c4cd0f022e1c9bc1dfe8559d.png"},{"id":97643308,"identity":"64abeb00-7b2a-4776-85af-38b72a6f93f7","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"png","order_by":52,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":11419,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/9b751df61ce55ab79cb440f3.png"},{"id":97673638,"identity":"041290e9-4270-4f40-93d6-d677dafa829a","added_by":"auto","created_at":"2025-12-08 09:40:53","extension":"png","order_by":53,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59418,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/54bad1d07d75c51aa022d629.png"},{"id":97674198,"identity":"2ec7bcf9-66fd-4307-a20a-b1355cd771e9","added_by":"auto","created_at":"2025-12-08 09:42:36","extension":"png","order_by":54,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":97563,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/c053a57f5fb6c214b636d9fd.png"},{"id":97643282,"identity":"bb8f5589-4f2d-4018-a2d4-a65dc31cccfc","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":55,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":13719,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/812c0a398288c8470f9c67b6.png"},{"id":97643306,"identity":"279d55fe-7ec5-46c0-96d2-167194b5dc3e","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"png","order_by":56,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":239,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage121.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/6a476269e5d412f6186f9f3d.png"},{"id":97673870,"identity":"c5c6b83a-175e-43e0-a0d5-41c736e8879d","added_by":"auto","created_at":"2025-12-08 09:41:42","extension":"png","order_by":57,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":207,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/6065f4e423c669151e252ba1.png"},{"id":97643314,"identity":"5c6fb547-d61a-4697-8c1b-56ccc5041fc3","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"png","order_by":58,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":283,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage72.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/02b2d77ea9bb3572bf215315.png"},{"id":97643276,"identity":"37c027e8-e6c4-44f0-9298-a01c733c718d","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":59,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":242,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage73.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/ded694c6d03cf21b03b68893.png"},{"id":97673919,"identity":"bc3eda30-6643-432b-b5a0-f91d11a25bb1","added_by":"auto","created_at":"2025-12-08 09:41:53","extension":"png","order_by":60,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":227,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage74.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/1771381f896d6e19f9d5d183.png"},{"id":97643298,"identity":"0930ae0c-daf5-4fc3-8331-c618fa65cdf3","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":61,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":193,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage75.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/59e84f21cd517280f3cfc95a.png"},{"id":97643300,"identity":"58109417-2ff2-493f-82ba-8319be629d2b","added_by":"auto","created_at":"2025-12-08 03:57:55","extension":"png","order_by":62,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":221,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage90.png","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/51c96528bc72fb4d89e28643.png"},{"id":97674303,"identity":"2100b9d7-d298-43ed-8c8a-a38121aa780e","added_by":"auto","created_at":"2025-12-08 09:42:56","extension":"xml","order_by":63,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":138359,"visible":true,"origin":"","legend":"","description":"","filename":"ba047de5978c44d0b8088d7b5955ea021structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/b5a8c3f496bceb3380077056.xml"},{"id":97643310,"identity":"9e32af1d-8046-460f-950b-a47a94773c47","added_by":"auto","created_at":"2025-12-08 03:57:56","extension":"html","order_by":64,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":158922,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1/fff99c76bad3248434cfb9df.html"},{"id":97678684,"identity":"658dd6f3-d331-4617-94c6-da6c363c74eb","added_by":"auto","created_at":"2025-12-08 09:55:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1363005,"visible":true,"origin":"","legend":"","description":"","filename":"ParameterEstimationof3DGTDModelBasedonaMultiNeuralNetwork.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8209921/v1_covered_23bbabea-57b6-4330-95da-60cfcaa5e19d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Parameter Estimation of 3D-GTD Model Based on a Multi-Neural Network","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":"Three-dimensional geometrical theory of diffraction(3D-GTD) model, multi-neural network, scattering center parameters, self-generated dataset","lastPublishedDoi":"10.21203/rs.3.rs-8209921/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8209921/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this article, a novel parameter estimation method of three-dimensional geometrical theory of diffraction(3D-GTD) model based on a multi-neural network is proposed. By leveraging multi-view one-dimensional geometrical theory of diffraction(1D-GTD) parameters as input, the three-branch neural network simultaneously estimates 3D scattering center parameters\u0026mdash;position, intensity, and type. Position reconstruction branch employs geometric encoding and gated fusion for joint feature extraction, combined with hierarchical attention and coordinate regression. Scattering intensity estimation branch achieves efficient feature aggregation via multi-level convolutional layers and parameter sharing mechanism, enabling high-precision intensity parameter estimation while ensuring model lightweight. Type identification branch establishes a mapping from numerical features to categorical indices, which converts the regression task into a classification task that conforms to discrete value constraints. It employs a sub-channel processing architecture and a shared multi-layer perceptron (MLP) to effectively aggregate multi-view predictive information, thereby achieving accurate identification of scattering center types. To address the challenge of difficult acquisition of training data, we construct a self-generated dataset with random characteristics, thereby enhancing the generalization performance of the network. Experimental results show the proposed method outperforms traditional approaches in estimation accuracy across different signal-to-noise ratio (SNR) levels and computational efficiency.\u003c/p\u003e","manuscriptTitle":"Parameter Estimation of 3D-GTD Model Based on a Multi-Neural Network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-08 03:57:49","doi":"10.21203/rs.3.rs-8209921/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-22T12:13:42+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-19T12:08:45+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-17T13:57:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"78376556557295108426100629584744343309","date":"2025-12-16T14:25:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"248945651255874005271074077746628722912","date":"2025-12-16T14:13:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"217729917795667527287447559290289006926","date":"2025-12-14T10:30:01+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-04T05:18:30+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-01T09:33:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-28T04:02:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-28T04:02:03+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-11-26T07:13:57+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":"07fa2b5b-bafc-4046-ae7a-5b8a5eb0c17b","owner":[],"postedDate":"December 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":59209490,"name":"Physical sciences/Engineering"},{"id":59209491,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2025-12-22T12:47:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-08 03:57:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8209921","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8209921","identity":"rs-8209921","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}