{"id":"https://openalex.org/W4401226379","doi":"https://doi.org/10.1137/23m1556605","title":"An Alternating Flux Learning Method for Multidimensional Nonlinear Conservation Laws","display_name":"An Alternating Flux Learning Method for Multidimensional Nonlinear Conservation Laws","publication_year":2024,"publication_date":"2024-08-01","ids":{"openalex":"https://openalex.org/W4401226379","doi":"https://doi.org/10.1137/23m1556605"},"language":"en","primary_location":{"id":"doi:10.1137/23m1556605","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1556605","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100734612","display_name":"Qing Li","orcid":"https://orcid.org/0000-0002-8796-8887"},"institutions":[{"id":"https://openalex.org/I92008406","display_name":"University of Stavanger","ror":"https://ror.org/02qte9q33","country_code":"NO","type":"education","lineage":["https://openalex.org/I92008406"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Qing Li","raw_affiliation_strings":["Department of Energy and Petroleum, Group of Computational Engineering, University of Stavanger, Stavanger, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy and Petroleum, Group of Computational Engineering, University of Stavanger, Stavanger, Norway","institution_ids":["https://openalex.org/I92008406"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078812575","display_name":"Steinar Evje","orcid":"https://orcid.org/0000-0003-2174-4095"},"institutions":[{"id":"https://openalex.org/I4210134503","display_name":"Petroleum Technology Company (Norway)","ror":"https://ror.org/03d9q1m75","country_code":"NO","type":"company","lineage":["https://openalex.org/I4210134503"]},{"id":"https://openalex.org/I92008406","display_name":"University of Stavanger","ror":"https://ror.org/02qte9q33","country_code":"NO","type":"education","lineage":["https://openalex.org/I92008406"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Steinar Evje","raw_affiliation_strings":["Corresponding author.\u00a0Department of Energy and Petroleum, Group of Computational Engineering, University of Stavanger, Stavanger, Norway"],"raw_orcid":"https://orcid.org/0000-0003-2174-4095","affiliations":[{"raw_affiliation_string":"Corresponding author.\u00a0Department of Energy and Petroleum, Group of Computational Engineering, University of Stavanger, Stavanger, Norway","institution_ids":["https://openalex.org/I92008406","https://openalex.org/I4210134503"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100734612"],"corresponding_institution_ids":["https://openalex.org/I92008406"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11507954,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"4","first_page":"C421","last_page":"C447"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"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":0.9994999766349792,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.986299991607666,"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/conservation-law","display_name":"Conservation law","score":0.8443928360939026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7504861354827881},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6633007526397705},{"id":"https://openalex.org/keywords/flux","display_name":"Flux (metallurgy)","score":0.557945728302002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4716731011867523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4117082953453064},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.38671639561653137},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3681012988090515},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11306697130203247},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.10252109169960022}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8443928360939026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7504861354827881},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6633007526397705},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.557945728302002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4716731011867523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4117082953453064},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38671639561653137},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3681012988090515},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11306697130203247},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.10252109169960022},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1556605","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23m1556605","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320315101","display_name":"Universitetet i Stavanger","ror":"https://ror.org/02qte9q33"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1487887263","https://openalex.org/W1571871558","https://openalex.org/W1993076613","https://openalex.org/W2000084698","https://openalex.org/W2005126631","https://openalex.org/W2041763847","https://openalex.org/W2573798107","https://openalex.org/W2588198210","https://openalex.org/W2800504875","https://openalex.org/W2887661471","https://openalex.org/W2899283552","https://openalex.org/W2903660960","https://openalex.org/W3047245470","https://openalex.org/W3096831136","https://openalex.org/W3105735469","https://openalex.org/W3111914315","https://openalex.org/W3183994952","https://openalex.org/W4223906621","https://openalex.org/W4301116206","https://openalex.org/W4312425695"],"related_works":["https://openalex.org/W1995118522","https://openalex.org/W64916076","https://openalex.org/W2090020940","https://openalex.org/W4364366001","https://openalex.org/W2565229889","https://openalex.org/W1072895066","https://openalex.org/W2894005322","https://openalex.org/W4213003931","https://openalex.org/W2607078461","https://openalex.org/W2383959235"],"abstract_inverted_index":{".In":[0],"a":[1,27,48,65,111,138],"recent":[2],"work":[3,58],"[Q.":[4],"Li":[5],"and":[6,47,99,107,172,182],"S.":[7],"Evje,":[8],"Netw.":[9],"Heterog.":[10],"Media,":[11],"18":[12],"(2023),":[13],"pp.":[14],"48\u201379],":[15],"it":[16],"was":[17],"explored":[18],"how":[19],"to":[20,38,60,64,87],"identify":[21,165],"the":[22,40,82,85,88,96,121,161,166,175],"unknown":[23,97],"flux":[24,42,122,134,143,169],"function":[25],"in":[26,92,174],"one-dimensional":[28],"scalar":[29,67],"conservation":[30,68,185],"law.":[31],"Key":[32],"ingredients":[33],"are":[34,128,180],"symbolic":[35],"neural":[36,188],"networks":[37],"represent":[39],"candidate":[41,142],"functions,":[43,123],"entropy-satisfying":[44],"numerical":[45,192],"schemes,":[46],"proper":[49],"combination":[50],"of":[51,56,81,95,120,141],"initial":[52],"data.":[53],"The":[54],"purpose":[55],"this":[57,62],"is":[59,114,149],"extend":[61],"methodology":[63],"two-dimensional":[66],"law":[69],"(":[70],"\\(*\\)":[71],")":[72],"\\(u_t":[73],"+":[74,76],"f(u)_x":[75],"g(u)_y=0\\)":[77],".":[78,101],"Straightforward":[79],"extension":[80],"method":[83,162],"from":[84,105,146],"1D":[86],"2D":[89,126],"problem":[90],"results":[91],"poor":[93],"identification":[94,119],"\\(f(u)\\)":[98],"\\(g(u)\\)":[100],"Relying":[102],"on":[103],"ideas":[104],"joint":[106,147],"alternating":[108,133,153],"equations":[109,194,196],"training,":[110],"learning":[112],"strategy":[113],"designed":[115],"that":[116,160],"enables":[117],"accurate":[118],"even":[124],"when":[125,178],"observations":[127],"sparse.":[129],"It":[130],"involves":[131],"an":[132,152],"training":[135,148,155],"approach":[136],"where":[137],"first":[139],"set":[140],"functions":[144,170],"obtained":[145],"improved":[150],"through":[151],"direction-dependent":[154],"strategy.":[156],"Numerical":[157],"investigations":[158],"demonstrate":[159],"can":[163],"effectively":[164],"true":[167],"underlying":[168],"\\(f\\)":[171],"\\(g\\)":[173],"general":[176],"case":[177],"they":[179],"nonconvex":[181],"unequal.Keywordsscalar":[183],"nonlinear":[184],"lawsymbolic":[186],"multilayer":[187],"networkentropy":[189],"consistent":[190],"discrete":[191],"schemejoint":[193],"trainingalternating":[195],"trainingMSC":[197],"codes68Q2568R1068U05":[198]},"counts_by_year":[],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}
