[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127515-en":3,"doc-seo-127515-105":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},127515,13056712833777,"Logic","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Bayesian averaging for ground state masses of atomic nuclei - Machine Learning approach","Global predictions of the ground state mass of atomic nuclei are constructed using a hybrid strategy that merges precision nuclear experimental measurements with theoretical predictions for nuclei without direct data. A probabilistic neural network is trained on this combined dataset, while a physics-based loss function refines the learned solutions. The resulting Bayesian-averaged predictions match the testing set well and include well-quantified uncertainties essential for modern scientific applications. Extrapolation behavior is analyzed, including how uncertainty grows in regions far from measurements.","arXiv :2304 .08546v1 [nucl-th] 17 Apr 2023  \nBayesian averaging for ground state masses of atomic nuclei in a Machine Learning  \napproach  \nM. R. Mumpower,􀀃 T. M. Sprouse, A. E. Lovell, and A. T. Mohan  \nTheoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA  \nM. Li  \nClemson University, Department of Physics and Astronomy, Clemson, SC 29634-0978, USA and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA  \nB. S. Meyer  \nClemson University, Department of Physics and Astronomy, Clemson, SC 29634-0978, USA  \n(Dated: April 19, 2023)  \nWe present global predictions of the ground state mass of atomic nuclei based on a novel Machine Learning (ML) algorithm. We combine precision nuclear experimental measurements together with theoretical predictions of unmeasured nuclei. This hybrid data set is used to train a probabilistic neural network. In addition to training on this data, a physics-based loss function is employed to help re􀀌ne the solutions. The resultant Bayesian averaged predictions have excellent performance compared to the testing set and come with well-quanti􀀌ed uncertainties which are critical for contemporary scienti􀀌c applications. We assess extrapolations of the model's predictions and estimate the growth of uncertainties in the region far from measurements.  \nI. INTRODUCTION  \nMass is a de􀀌ning quantity of an atomic nucleus and appears ubiquitously in research e􀀋orts ranging from technical applications to scienti􀀌c studies such as the synthesis of the heavy elements in astrophysical environments [1, 2] . While accurate nuclear data of masses is available for nuclei that are relatively stable, the same is not true for nuclei farther away from beta stability because measurements on radioactive nuclei are exceedingly challenging [3] . As a consequence, theoretical models of atomic nuclei are required for extrapolations used in present-day scienti􀀌c applications [4] .  \nThe goal of theoretical nuclear models is to describe all atomic nuclei (from light to heavy) using fundamental interactions. Attainment of this challenging goal remains elusive, however, due to the sheer complexity of modeling many-body systems with Quantum Chromodynamics [5] . To understand the range of nuclei that may exist in nature, mean-􀀌eld approximations are often made which simplify complex many-body dynamics into a non-interacting system of quasi-particles where remaining residual interactions can be added as perturbations [6] . A consequence of this approximation is that current nuclear modeling e􀀋orts are unable to describe the rich correlations that are found across the chart of nuclides.  \nIn contrast, Machine Learning (ML) based approaches do not have to rely on the assumption of modeling nuclei from a mean-􀀌eld. This provides freedom in 􀀌nding solutions that contemporary modeling may not be capable of ascertaining. Furthermore, Bayesian approaches to ML a􀀋ord the ability to associate predictions with uncertainties [7, 8] . Such tasks are more di􀀎cult to achieve in modern nuclear modeling due to relatively higher computational costs.  \nML approaches in nuclear physics were pioneered by J.W. Clark and colleagues [9, 10] . These studies were the 􀀌rst to show that networks could approximate stable nuclei, learn to predict masses and analyze nuclear systematics of separation energies as well as spin-parity assignments [11, 12] . Powered by open-source frameworks, research into ML methods has seen a recent resurgence in nuclear physics [13] . ML approaches have shown promise in optimizing data and experiments [14], building surrogate models of density functional theory [15], and describing quantum many-body wave functions for light nuclei[16, 17] .  \nSeveral research groups are actively pursuing the problem of describing nuclear systems with ML from a more data-centric approach. These e􀀋orts currently attempt to improve existing nuclear models by adding correction terms [18] . Gaussian Proces","cbCainJxPR8UAqbA","https://ap.wps.com/l/cbCainJxPR8UAqbA","pdf",894534,1,15,"English","en",105,"# Introduction\n## Nuclear mass modeling challenges\n## Machine learning and Bayesian approaches\n# Methods\n## Mixture Density Network","[{\"question\":\"How is the training dataset for nuclear ground state masses built in this work?\",\"answer\":\"Precision experimental mass measurements are combined with theoretical predictions for nuclei that have not been measured. This hybrid dataset trains the probabilistic neural network.\"},{\"question\":\"What role does the physics-based loss function play?\",\"answer\":\"A physics-based loss function is added during training to refine and improve the probabilistic neural network’s solutions beyond what data alone provides.\"},{\"question\":\"How are uncertainties handled, especially for extrapolations away from measured nuclei?\",\"answer\":\"The method produces Bayesian-averaged predictions with well-quantified uncertainties. It also evaluates extrapolation quality and estimates how uncertainties expand in regions far from available measurements.\"}]","Bayesian averaging for ground state masses of atomic nuclei - Machine Learning approach | PDF",1785939647,38,{"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},"bayesian-averaging-for-ground-state-masses-of-atomic-nuclei-machine-learning-approach","",{"@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/bayesian-averaging-for-ground-state-masses-of-atomic-nuclei-machine-learning-approach/127515/",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","2026-08-22","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},"How is the training dataset for nuclear ground state masses built in this work?","Question",{"text":76,"@type":77},"Precision experimental mass measurements are combined with theoretical predictions for nuclei that have not been measured. This hybrid dataset trains the probabilistic neural network.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What role does the physics-based loss function play?",{"text":81,"@type":77},"A physics-based loss function is added during training to refine and improve the probabilistic neural network’s solutions beyond what data alone provides.",{"name":83,"@type":74,"acceptedAnswer":84},"How are uncertainties handled, especially for extrapolations away from measured nuclei?",{"text":85,"@type":77},"The method produces Bayesian-averaged predictions with well-quantified uncertainties. It also evaluates extrapolation quality and estimates how uncertainties expand in regions far from available measurements.","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"]