[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119579-en":3,"doc-seo-119579-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"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},119579,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Machine learning mapping of lattice correlated data - research paper","A machine learning regression framework is developed to lower the computational cost of disconnected diagrams in lattice QCD. The approach learns a mapping between fermionic loop results evaluated at different quark masses and gradient-flow times. Training uses only a small subset of the full data set while exploiting translational invariance. The resulting predictions remain consistent with uncertainties comparable to full-ensemble calculations, delivering substantial computational gains. Gradient flow is used to improve signal quality and renormalization behavior.","arXiv :2402 .07450v3 [hep-lat] 30 Aug 2024  \nTTK-24-07  \nMachine learning mapping of lattice correlated data  \nJangho Kima , Giovanni Pederivab , Andrea Shindlerc,d,e  \na Institute for Advanced Simulation (IAS-4) - Forschungszentrum  \nJülich, Wilhelm-Johnen-Straße, Jülich, 52428, Germany  \nbJülich Supercomputing Centre (JSC) & Center for Advanced Simulation and Analytics  \n(CASA), Wilhelm-Johnen-Straße, Jülich, 52428, Germany  \nc Institute for Theoretical Particle Physics and Cosmology, TTK, RWTH Aachen University, Sommerfeldstr.  \n16, Aachen, 52074, Germany  \nd Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA e Department of Physics, University of California, Berkeley, CA 94720, USA  \nAbstract  \nWe discuss a machine learning (ML) regression model to reduce the computational cost of disconnected diagrams in lattice QCD calculations. This method creates a mapping between the results of fermionic loops computed at different quark masses and flow times. The ML mapping, trained with just a small fraction of the complete data set, makes use of translational invariance and provides consistent result with comparable uncertainties over the calculation done over the whole ensemble, resulting ina significant computational gain.  \nKeywords: Lattice QCD, Fermionic Disconnected Diagrams, Machine Learning  \n1. Introduction  \nOne of the computational challenges in lattice QCD calculations lies in the determination of the quark propagator, which not only serves as the foundation for calculating any fermionic correlation function but is also required in generating gauge ensembles with dynamical quarks. Computing the quark propagator involves inverting a very large sparse matrix representing the lattice Dirac operator. Fermionic disconnected diagrams appear in most hadron matrix element calculations, as well as studies of flavor singlet channels, and standard methods for their calculation are based on stochastic estimates, which are usually computationally expensive.  \nIn this study, we aim to leverage on recent advancements in Machine Learning (ML) applications to lattice QCD calculations used to reconstruct the Euclidean time dependence of complex observables by correlating them with simpler functions [1] . The findings of Ref. [1] highlighted that ML techniques can effectively map various correlation functions, such as 2-and 3-point functions when utilizing the same Markov chain. Building upon this observation we extend this approach to calculate fermion disconnected diagrams. These calculations involve the manipulation of significant amounts of data, dependent on the amount of stochastic sources and gauge configurations employed.  \nMoreover, exploiting the inherent translational invariance of the lattice theory, we augment our dataset to thoroughly investigate correlations. Utilizing numerous stochastic sources and  \nEmail addresses: [j.kim@fz-juelich.de](j.kim@fz-juelich.de) (Jangho Kim), g.pederiva@fz-juelich.de (Giovanni Pederiva), [shindler@physik.rwth-aachen.de](shindler@physik.rwth-aachen.de) (Andrea Shindler)  \ntranslational invariance, we establish both training and bias-correction sets, thereby strengthening the robustness and precision of our analyses.  \nThe gradient flow [2, 3] provides a favorable regulator of short-distance singularities due to its reduced operator mixing, essentially trading power divergent lattice spacing effects with a milder finite 1/t dependence. By keeping the flow time t fixed, one can then perform the continuum limit with no renormalization ambiguities. An example of the advantage of the use of the Gradient Flow is the simplified calculation of the quark content of nucleons [4, 5] or the resolution of the problem of power divergences for higher dimensional operators [6] . The application of the gradient flow to the calculation of fermionic disconnected diagrams is beneficial both to simplify the renormalization and to improve the signal-to-noise ratio.  \nIn Sec. 2","cbCaisSaGeoY4U9W","https://ap.wps.com/l/cbCaisSaGeoY4U9W","pdf",1296975,1,17,"English","en",105,"# Introduction\n# Fermionic disconnected diagrams\n## Stochastic estimation for all-to-all propagators\n# Correlation analysis and bias correction\n# ML algorithm and results","[{\"question\":\"What problem does the machine learning model address in lattice QCD?\",\"answer\":\"It reduces the computational cost associated with disconnected diagrams by learning a regression mapping for fermionic loop results.\"},{\"question\":\"How does the method relate data across different quark masses and flow times?\",\"answer\":\"It builds a mapping between fermionic loop outcomes computed at varying quark masses and gradient-flow times, enabling consistent predictions under fixed flow-time training.\"},{\"question\":\"Why is gradient flow important in this study?\",\"answer\":\"Gradient flow regulates short-distance singularities, simplifies renormalization, and improves the signal-to-noise ratio for fermionic disconnected diagram calculations.\"}]","Machine learning mapping of lattice correlated data - research paper | PDF",1785725094,43,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-mapping-of-lattice-correlated-data-research-paper","",{"@graph":36,"@context":85},[37,54,68],{"@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-mapping-of-lattice-correlated-data-research-paper/119579/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the machine learning model address in lattice QCD?","Question",{"text":75,"@type":76},"It reduces the computational cost associated with disconnected diagrams by learning a regression mapping for fermionic loop results.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method relate data across different quark masses and flow times?",{"text":80,"@type":76},"It builds a mapping between fermionic loop outcomes computed at varying quark masses and gradient-flow times, enabling consistent predictions under fixed flow-time training.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is gradient flow important in this study?",{"text":84,"@type":76},"Gradient flow regulates short-distance singularities, simplifies renormalization, and improves the signal-to-noise ratio for fermionic disconnected diagram calculations.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]