[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128088-en":3,"doc-seo-128088-105":31,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128088,687207022233,"Riley","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Cosmic topology. Part IVa - Classification of manifolds using machine learning: a case study with small toroidal universes","Non-trivial spatial topology of the Universe can produce observable signatures in the cosmic microwave background. The study evaluates multiple machine-learning approaches to classify harmonic-space realizations of the microwave background for Euclidean E1 topology, specifically a 3-torus with a cubic fundamental domain whose size scale is much smaller than the last-scattering surface diameter. The work represents an early step toward machine-learning-based cosmic-topology classification and likelihood-free inference of topological parameters, reporting very high classification accuracy in favorable scale regimes.","Journal of Cosmology and Astroparticle Physics  \nPAPER • OPEN ACCESS  \nCosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes  \nTo cite this article: Andrius Tamosiunas et al JCAP09(2024)057  \nYou may also like  \n-J Walcher  \n-Erratum: Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches  \nDeyan P. Mihaylov, Yashar Akrami, Craig  \nJ. Copi et al.  \n-Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds  \nJohannes R. Eskilt, Yashar Akrami, Stefano Anselmi et al.  \nView the article online for updates and enhancements.  \nThis content was downloaded from IP address [150.244.223.183](150.244.223.183) on 04/03/2025 at 11:30  \nJA  Calosmology and Astroparticle Physics  \nReceived: April 10, 2024  \nRevised: August 10, 2024  \nAccepted: August 20, 2024  \nPublished: September 25, 2024  \nCosmic topology. Part IVa . Classification of manifolds using machine learning: a case study with small toroidal universes  \nThe COMPACT collaboration  \nAndrius Tamosiunas  ,a Fernando Cornet-Gomez  ,a Yashar Akrami  ,b,a,c Stefano Anselmi  ,d,e,f Javier Carrón Duque  ,b Craig J. Copi  ,a  \nJohannes R. Eskilt  ,g,c Özenç Güngör  ,a Andrew H. Jaffe  ,c Arthur Kosowsky  h  \n,  \nMikel Martin Barandiaran  ,b James B. Mertens  ,a Deyan P. Mihaylov  ,a Thiago S. Pereira  ,i Samanta Saha  ,a Amirhossein Samandar  ,a  \nGlenn D. Starkman  ,a Quinn Taylor a and Valeri Vardanyan j  \naCERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, U. S. A.  \nbInstituto de Física Teórica (IFT) UAM-CSIC,  \nCampus de Cantoblanco UAM, C/ Nicolás Cabrera 13 –15, Madrid 28049, Spain cAstrophysics Group & Imperial Centre for Inference and Cosmology, Department of Physics,  \nImperial College London, Blackett Laboratory,  \nPrince Consort Road, London SW7 2AZ, United Kingdom  \ndINFN, Sezione di Padova,  \nvia Marzolo 8, Padova I-35131, Italy  \neDipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova, via Marzolo 8, Padova I-35131, Italy  \nf Laboratoire Univers et Théories, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS,  \nMeudon F-92190, France  \ng Institute of Theoretical Astrophysics, University of Oslo, P. O. Box 1029 Blindern, Oslo N-0315, Norway  \n© 2024 The Author(s) . Published by IOP Publishing  \nLtd on behalf of Sissa Medialab. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \n[https://doi.org/10.1088/1475-7516/2024/09/057](https://doi.org/10.1088/1475-7516/2024/09/057)  \nJ CAP09(2024)057  \nh Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.  \ni Departamento de Física, Universidade Estadual de Londrina,  \nRod. Celso Garcia Cid, Km 380, Londrina 86057-970, Paraná, Brazil  \njKavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo,  \nChiba 277-8583, Japan  \nE-mail: [andrius.tamosiunas@case.edu](andrius.tamosiunas@case.edu) , [fernando.cornetgomez@case.edu](fernando.cornetgomez@case.edu) ,  \n[yashar.akrami@csic.es](yashar.akrami@csic.es) , [stefano.anselmi@pd.infn.it](stefano.anselmi@pd.infn.it) ,  \n[javier.carron@csic.es](javier.carron@csic.es) , [craig.copi@case.edu](craig.copi@case.edu) , [j.r.eskilt@astro.uio.no](j.r.eskilt@astro.uio.no) ,  \n[ozenc.gungor@case.edu](ozenc.gungor@case.edu) , [a.jaffe@imperial.ac.uk](a.jaffe@imperial.ac.uk) , [kosowsky@pitt.edu](kosowsky@pitt.edu) ,  \n[mikel.martin@uam.es](mikel.martin@uam.es) , [james.mertens@case.edu](james.mertens@case.edu) , [deyan.mihaylov@case.edu](deyan.mihaylov@case.edu) ,  \n[tspereira@uel.br](tspereira@uel.br) , [samanta.saha@case.edu](samanta.saha@case.edu) , [amirhossein.saman","cbCaifquBDgufVI4","https://ap.wps.com/l/cbCaifquBDgufVI4","pdf",2634850,3,1,39,"English","en",105,"# Abstract\n## Cosmic microwave background signatures from spatial topology\n## Machine-learning classification of harmonic-space realizations\n## Euclidean E1 topology and 3-torus test cases\n## Outlook: topology classification and likelihood-free inference","[{\"question\":\"What kind of cosmic signal motivates this research?\",\"answer\":\"Non-trivial spatial topology of the Universe can generate measurable signatures in the cosmic microwave background.\"},{\"question\":\"Which topology and geometric setup are used for the case study?\",\"answer\":\"The study focuses on Euclidean E1 topology, modeling the Universe as a 3-torus with a cubic fundamental domain smaller than the last-scattering surface diameter.\"},{\"question\":\"What is the goal of using machine learning here?\",\"answer\":\"To classify harmonic-space realizations of the microwave background and support development toward likelihood-free inference of topological parameters.\"}]","Cosmic topology. Part IVa - Classification of manifolds using machine learning: a case study with small toroidal universes | PDF",1785944733,98,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"cosmic-topology-part-iva-classification-of-manifolds-using-machine-learning-a-case-study-with-small-toroidal-universes-128088","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":20},"https://docshare.wps.com/document/research-report/",{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/cosmic-topology-part-iva-classification-of-manifolds-using-machine-learning-a-case-study-with-small-toroidal-universes-128088/128088/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-25","2026-08-05",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},"What kind of cosmic signal motivates this research?","Question",{"text":76,"@type":77},"Non-trivial spatial topology of the Universe can generate measurable signatures in the cosmic microwave background.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which topology and geometric setup are used for the case study?",{"text":81,"@type":77},"The study focuses on Euclidean E1 topology, modeling the Universe as a 3-torus with a cubic fundamental domain smaller than the last-scattering surface diameter.",{"name":83,"@type":74,"acceptedAnswer":84},"What is the goal of using machine learning here?",{"text":85,"@type":77},"To classify harmonic-space realizations of the microwave background and support development toward likelihood-free inference of topological parameters.","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":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]