[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122637-en":3,"doc-seo-122637-105":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},122637,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Deducing Neutron Star Equation of State from Telescope Spectra with Machine-learning-derived Likelihoods","Neutron star interiors provide a unique probe of matter at extreme densities and temperatures, but their internal pressure-density structure cannot be directly observed. Telescope spectra reflect macroscopic properties that are tied to the equation of state through a complex and partially intractable likelihood. This work replaces untractable likelihood components with machine learning models trained on simulated neutron stars, enabling maximum a posteriori estimation and full parameter scans from observed spectra. In realistic tests, the method improves parameter residual widths by 11.8% over pure regression and releases neural networks for fast simulation and inference.","arXiv :2305 .07442v2 [ astro-ph .HE] 17 May 2023  \nDeducing Neutron Star Equation of State from Telescope Spectra with Machine-learning-derived Likelihoods  \nDelaney Farrell, 1 Pierre Baldi,2 Jordan Ott,2 Aishik Ghosh,3, 4 Andrew W. Steiner,5, 6 Atharva Kavitkar,7 Lee Lindblom,8 Daniel Whiteson,3 and Fridolin Weber 1, 8  \n1 Department of Physics, San Diego State University, San Diego, CA 92115, United States  \n2 Department of Computer Science, University of California Irvine, Irvine, California 92697, USA  \n3 Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, USA  \n4 Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  \n5 Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA  \n6 Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA  \n7Department of Computer Science, TU Kaiserslautern, Germany  \n8 Center for Astrophysics and Space Sciences, University of California at San Diego, San Diego, CA 92093, United States  \nThe interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which a􀀋ectsthe spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting di􀀎culties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11 .8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.  \nContents  \nI. Introduction 2  \nII. Background 3  \nIII. Machine Learning 4  \nIV. Training Data 4  \nA. Generation of Equation of State 4  \nB. Modeling Spectra 5  \nC. Nuisance Parameters 5  \nV. Machine-Learning Derived Likelihood Calculation 5  \nVI. Stellar Mass and Radius Inference 6  \nA. Learning the Model f for Stellar Spectra 7  \nB. Results 7  \nVII. Equation of State Inference 9  \nA. Learning the Model h􀀕 [M ] for Stellar Radius 12  \nB. Results 13  \nVIII. Discussion 15  \nIX. Conclusion 15  \nX. Acknowledgements 16  \n2  \nReferences 17  \nI. INTRODUCTION  \nNeutron stars are valuable astrophysical laboratories for studying matter under extreme conditions. With masses generally between 1 to 2 M􀀌 and radii between 10 and 15 km, the inner regions of these neutron-rich stars can reach density regimes well beyond those accessible in terrestrial laboratories. Matter at such high densities can potentially experience transitions to stable but unusual states of matter such as exotic baryons made of hyperons and 􀀁 isobars [1{ 5]; decon􀀌ned up, down, and strange quarks [6, 7]; color superconducting phases [8{10]; or Bose-Einstein condensates made of negatively charged pions or K 􀀀 mesons [11{15] . A better understanding of the internal composition of these stars would shed light on many areas of current interest, including various astrophysical phenomena such as core-collapse supernovae [16] and binary star mergers [17], nuclear laboratory physics, QCD and relativistic gravity, as well as the early Universe. A long-standing issue in ex","cbCait0Bu09r1Vke","https://ap.wps.com/l/cbCait0Bu09r1Vke","pdf",2413519,1,18,"English","en",105,"# Introduction\n# Background\n# Machine Learning\n## Training Data\n## Machine-Learning Derived Likelihood Calculation\n# Stellar Mass and Radius Inference\n## Equation of State Inference\n# Discussion\n# Conclusion\n# Acknowledgements\n# References","[{\"question\":\"Why is inferring neutron star equation of state from telescope spectra difficult?\",\"answer\":\"Because the mapping from internal pressure-density structure to observed spectra involves likelihood elements that are complex and not straightforward to compute or invert.\"},{\"question\":\"How does the method use machine learning in the likelihood calculation?\",\"answer\":\"It trains machine learning models on simulated neutron-star samples to replace intractable parts of the likelihood, producing a machine-learning-derived likelihood for inference.\"},{\"question\":\"What inference tasks are demonstrated in the study?\",\"answer\":\"The authors infer stellar mass and radius from an individual spectrum and infer equation-of-state parameters from sets of spectra, using maximum a posteriori estimation and full scans.\"}]","Deducing Neutron Star Equation of State from Telescope Spectra with Machine-learning-derived Likelihoods | 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is inferring neutron star equation of state from telescope spectra difficult?","Question",{"text":75,"@type":76},"Because the mapping from internal pressure-density structure to observed spectra involves likelihood elements that are complex and not straightforward to compute or invert.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the method use machine learning in the likelihood calculation?",{"text":80,"@type":76},"It trains machine learning models on simulated neutron-star samples to replace intractable parts of the likelihood, producing a machine-learning-derived likelihood for inference.",{"name":82,"@type":73,"acceptedAnswer":83},"What inference tasks are demonstrated in the study?",{"text":84,"@type":76},"The authors infer stellar mass and radius from an individual spectrum and infer equation-of-state parameters from sets of spectra, using maximum a posteriori estimation and full 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