{"id":"https://openalex.org/W3168560824","doi":"https://doi.org/10.1137/21m1423956","title":"Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures","display_name":"Machine Learning Moment Closure Models for the Radiative Transfer Equation II: Enforcing Global Hyperbolicity in Gradient-Based Closures","publication_year":2023,"publication_date":"2023-04-25","ids":{"openalex":"https://openalex.org/W3168560824","doi":"https://doi.org/10.1137/21m1423956","mag":"3168560824"},"language":"en","primary_location":{"id":"doi:10.1137/21m1423956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1423956","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2105.14410","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075922779","display_name":"Juntao Huang","orcid":"https://orcid.org/0000-0003-0527-7431"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Juntao Huang","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":"https://orcid.org/0000-0003-0527-7431","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002089116","display_name":"Yingda Cheng","orcid":"https://orcid.org/0000-0003-3229-2979"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yingda Cheng","raw_affiliation_strings":["Department of Mathematics, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083347493","display_name":"Andrew Christlieb","orcid":"https://orcid.org/0000-0002-5395-5455"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Christlieb","raw_affiliation_strings":["Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023916231","display_name":"Luke F. Roberts","orcid":"https://orcid.org/0000-0001-7364-7946"},"institutions":[{"id":"https://openalex.org/I4210094386","display_name":"National Superconducting Cyclotron Laboratory","ror":"https://ror.org/00qerpb33","country_code":"US","type":"facility","lineage":["https://openalex.org/I1311060795","https://openalex.org/I4210094386","https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luke F. Roberts","raw_affiliation_strings":["National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I4210094386"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023454820","display_name":"Wen\u2010An Yong","orcid":"https://orcid.org/0000-0003-4440-128X"},"institutions":[{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN","ES"],"is_corresponding":false,"raw_author_name":"Wen-An Yong","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China","Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"raw_orcid":"https://orcid.org/0000-0003-4440-128X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China","institution_ids":["https://openalex.org/I4210157032"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5075922779"],"corresponding_institution_ids":["https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":2.4195,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.87749023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"21","issue":"2","first_page":"489","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/radiative-transfer","display_name":"Radiative transfer","score":0.6899255514144897},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6044265031814575},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5113089084625244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4660545289516449},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4096105098724365},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.39554476737976074},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34279024600982666},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33503782749176025},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3233519196510315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3209455609321594},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.2832254469394684},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.127295583486557},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11881157755851746}],"concepts":[{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.6899255514144897},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6044265031814575},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5113089084625244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4660545289516449},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4096105098724365},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39554476737976074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34279024600982666},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33503782749176025},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3233519196510315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3209455609321594},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2832254469394684},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.127295583486557},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11881157755851746},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1423956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1423956","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2105.14410","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.14410","pdf_url":"https://arxiv.org/pdf/2105.14410","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2105.14410","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2105.14410","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2105.14410","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.14410","pdf_url":"https://arxiv.org/pdf/2105.14410","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2230619896","display_name":null,"funder_award_id":"DMS-2011838","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3592103773","display_name":null,"funder_award_id":"FA9550-19-1-0281","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3927447104","display_name":null,"funder_award_id":"FA9550-17-1-0394","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G46820549","display_name":null,"funder_award_id":"DMS-1912183","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5684507439","display_name":null,"funder_award_id":"12071246","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6968906821","display_name":null,"funder_award_id":"DE-SC0017955","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7158227453","display_name":null,"funder_award_id":"AST-2008004","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W250846124","https://openalex.org/W1553130110","https://openalex.org/W1971599530","https://openalex.org/W1973481688","https://openalex.org/W1979815750","https://openalex.org/W1990958245","https://openalex.org/W1998444595","https://openalex.org/W2039150507","https://openalex.org/W2045455639","https://openalex.org/W2050492048","https://openalex.org/W2057907461","https://openalex.org/W2060059568","https://openalex.org/W2067813500","https://openalex.org/W2074815274","https://openalex.org/W2076311850","https://openalex.org/W2117265445","https://openalex.org/W2131947874","https://openalex.org/W2159998136","https://openalex.org/W2239232218","https://openalex.org/W2265277793","https://openalex.org/W2270298035","https://openalex.org/W2326159504","https://openalex.org/W2476432869","https://openalex.org/W2512259174","https://openalex.org/W2585214286","https://openalex.org/W2626254232","https://openalex.org/W2803629276","https://openalex.org/W2896535417","https://openalex.org/W2899283552","https://openalex.org/W2958706811","https://openalex.org/W2963128411","https://openalex.org/W2963350904","https://openalex.org/W2963565448","https://openalex.org/W2964018859","https://openalex.org/W2964198882","https://openalex.org/W2974989237","https://openalex.org/W2984051592","https://openalex.org/W3010292040","https://openalex.org/W3040958695","https://openalex.org/W3044133295","https://openalex.org/W3092858841","https://openalex.org/W3098675970","https://openalex.org/W3102273638","https://openalex.org/W3102295111","https://openalex.org/W3109390220","https://openalex.org/W3118974691","https://openalex.org/W3129245939","https://openalex.org/W3161283735","https://openalex.org/W3161789250","https://openalex.org/W3204619447","https://openalex.org/W4237848465","https://openalex.org/W4309878915"],"related_works":["https://openalex.org/W315394019","https://openalex.org/W2923398117","https://openalex.org/W4309585848","https://openalex.org/W2265383332","https://openalex.org/W4328130279","https://openalex.org/W2105009749","https://openalex.org/W4299387245","https://openalex.org/W583262921","https://openalex.org/W2036721792","https://openalex.org/W2002342158"],"abstract_inverted_index":{"This":[0],"is":[1,66,96,117,122],"the":[2,19,36,39,50,54,59,85,89,107,115,125,131,134,138,143,153,158,162],"second":[3],"paper":[4,80],"in":[5,8,64,78],"a":[6,81,99],"series":[7],"which":[9,44],"we":[10,29],"develop":[11],"machine":[12],"learning":[13,49],"(ML)":[14],"moment":[15,51,61],"closure":[16,62,91,108,128,175],"models":[17],"for":[18,106],"radiative":[20],"transfer":[21],"equation":[22],"(RTE).":[23],"In":[24],"our":[25,171],"previous":[26],"work":[27],"\\cite{huang2021gradient},":[28],"proposed":[30],"an":[31],"approach":[32],"to":[33,69,83,97,147],"directly":[34],"learn":[35],"gradient":[37],"of":[38,88,133,170],"unclosed":[40],"high":[41],"order":[42],"moment,":[43],"performs":[45],"much":[46],"better":[47],"than":[48],"itself":[52],"and":[53,72,110,136,157,168],"conventional":[55],"$P_N$":[56],"closure.":[57],"However,":[58],"ML":[60,90,127,174],"model":[63],"\\cite{huang2021gradient}":[65],"not":[67],"able":[68],"guarantee":[70],"hyperbolicity":[71,87],"long":[73,165],"time":[74,166],"stability.":[75],"We":[76],"propose":[77],"this":[79],"method":[82],"enforce":[84],"global":[86],"model.":[92,176],"The":[93],"main":[94],"idea":[95],"seek":[98],"symmetrizer":[100],"(a":[101],"symmetric":[102],"positive":[103],"definite":[104],"matrix)":[105],"system,":[109],"derive":[111],"constraints":[112],"such":[113],"that":[114,124],"system":[116,129],"globally":[118,172],"symmetrizable":[119],"hyperbolic.":[120],"It":[121],"shown":[123],"new":[126],"inherits":[130],"dissipativeness":[132],"RTE":[135],"preserves":[137],"correct":[139],"diffusion":[140],"limit":[141],"as":[142],"Knunsden":[144],"number":[145],"goes":[146],"zero.":[148],"Several":[149],"benchmark":[150],"tests":[151],"including":[152],"Gaussian":[154],"source":[155],"problem":[156,160],"two-material":[159],"show":[161],"good":[163],"accuracy,":[164],"stability":[167],"generalizability":[169],"hyperbolic":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2021-06-22T00:00:00"}