[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117949-en":3,"doc-seo-117949-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117949,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Machine learning techniques for the ab initio Bravais lattice determination","Machine learning-based algorithms classify Bravais lattices directly from conventional X-ray diffraction diagrams, supporting crystallographic structural determination. The study focuses on the indexing stage, where information from reciprocal space must be mapped back to direct space, a task that is complex to invert. Multiple learning models are compared using 10-fold cross-validation, achieving 95.9% accuracy compared with 84% best results previously reported. A Bragg-position-based predictor estimates interplanar lattice distances and is validated on a complex case, demonstrating robustness to data imprecision and reduced input requirements under true ab initio conditions.","Received: 11 February 2022 Revised: 13 August 2022 Accepted: 25 September 2022  \nDOI: 10.1111/exsy.13160  \nO R IG INA L ARTI CLE  \nMachine learning techniques for the ab initio Bravais lattice determination  \nEsther-Lydia Silva-Ramírez 1 | Inmaculada Cumbrera-Conde 2 | Rafael Cano-Crespo 3 |  \nFrancisco-Luis Cumbrera 3  \n1Department of Computer Science and Engineering, University of Cádiz, Puerto Real, Spain  \n2Department of Private International Law, Macquarie University, Sydney, New South Wales, Australia  \n3Departamento de Física de la Materia Condensada, Universidad de Sevilla, Sevilla, Spain  \nCorrespondence  \nFrancisco-Luis Cumbrera, Departamento de Física de la Materia Condensada, Universidad de Sevilla, 41012 Sevilla, Spain.  \nEmail: [fcumbreras@us.es](fcumbreras@us.es)  \nAbstract  \nMachine learning-based algorithms have been widely applied recently in different areas due to its ability to solve problems in all fields. In this research, machine learning techniques classifying the Bravais lattices from a conventional X-ray diffraction diagram have been applied. Indexing algorithms are an essential tool of the preliminary protocol for the structural determination problem in crystallography. The task of reverting the obtained information in reciprocal lattice to direct space is a complex issue. As an alternative way to afford this problem, different machine learning algorithms have been applied and a comparison between them has been conducted. The obtained accuracy was 95.9% using 10-fold cross-validation (while the best result obtained so far has been 84%) . A model based on Bragg positions was our unique predictor, allowing us to obtain the set of the interplanar lattice distances. Our model was successfully checked with a complex example. In addition, our procedure incorporates the following advantages: robustness versus imprecision in data acquisition and reduction of the amount of necessary input data. This is the first time so far that such classification has been carried out in true ab initio condition.  \nKEYWOR DS  \nBravais lattices, crystallography, machine learning  \n1 | INTRODUCTION  \nMachine learning (ML) methods have achieved recently outstanding contributions in the materials research community as well as in other science domains (Agatonovic-Kustrin & Beresford, 2000; Bhadeshia, 1999; Dai et al., 2020; Scott et al., 2007; Sha & Edwards, 2007; Shetty et al., 1999; Woinaroschy et al., 2000; Zhang et al., 2008) . ML developments include methods which simulate brain working, for instance, artificial neural networks (ANN), or simulate human experience and draw conclusions as expert systems. Somehow, we can state that we are facing the solution of traditional complex problems with other different paradigm which offers greater speed and efficiency. The goal of our work is concerned to the solution of an outstanding problem of crystallography: the assignation of the Bravais lattice in structural determination. We will approach that key problem from conventional ML methods. Following, we address the task of laying out the fundamentals of such a problem.  \nCrystallography is the science that studies the atomic arrangements of crystalline solids. It is an axiomatic discipline that relies on two postulates: The postulates of Bravais and Schoenflies–Fedorov. First of them, known as micro-periodicity principle, states the foundation for  \nThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.  \n© 2022 The Authors. Expert Systems published by John Wiley & Sons Ltd.  \nExpert Systems. 2023;40:e13160 .  \n[https://doi.org/10.1111/exsy.13160](https://doi.org/10.1111/exsy.13160)  \n[wileyonlinelibrary.com/journal/exsy](wileyonlinelibrary.com/journal/exsy)  \n1 of 17  \n2 of 17  \nSILVA-RAMÍREZ  \nET AL.  \nFIGU","cbCaigpeuXFMGvrd","https://ap.wps.com/l/cbCaigpeuXFMGvrd","pdf",2413940,1,17,"English","en",105,"# Introduction\n## Crystallography fundamentals and Bravais lattices\n## Indexing algorithms and diffraction information\n## Motivation for machine learning ab initio classification","[{\"question\":\"How does the method identify Bravais lattices from X-ray diffraction data?\",\"answer\":\"It applies machine learning classifiers to conventional X-ray diffraction diagrams to assign the Bravais lattice. The approach uses learned patterns from diffraction reflections rather than relying solely on manual inversion.\"},{\"question\":\"What is the main technical challenge addressed in the study?\",\"answer\":\"The challenge is reverting reciprocal-lattice information obtained from diffraction back to direct-space structural parameters. The work treats this inversion problem using alternative machine learning models.\"},{\"question\":\"Which model performs best and what accuracy is reported?\",\"answer\":\"The best reported performance reaches 95.9% accuracy under 10-fold cross-validation, using a predictor based on Bragg positions. This model enables estimation of interplanar lattice distances and is checked with a complex example.\"}]","Machine learning techniques for the ab initio Bravais lattice determination | PDF",1785680497,43,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"machine-learning-techniques-for-the-ab-initio-bravais-lattice-determination","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-techniques-for-the-ab-initio-bravais-lattice-determination/117949/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-02",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"How does the method identify Bravais lattices from X-ray diffraction data?","Question",{"text":76,"@type":77},"It applies machine learning classifiers to conventional X-ray diffraction diagrams to assign the Bravais lattice. The approach uses learned patterns from diffraction reflections rather than relying solely on manual inversion.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What is the main technical challenge addressed in the study?",{"text":81,"@type":77},"The challenge is reverting reciprocal-lattice information obtained from diffraction back to direct-space structural parameters. The work treats this inversion problem using alternative machine learning models.",{"name":83,"@type":74,"acceptedAnswer":84},"Which model performs best and what accuracy is reported?",{"text":85,"@type":77},"The best reported performance reaches 95.9% accuracy under 10-fold cross-validation, using a predictor based on Bragg positions. This model enables estimation of interplanar lattice distances and is checked with a complex example.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]