{"id":"https://openalex.org/W4392517081","doi":"https://doi.org/10.1137/22m1537333","title":"Learning the Dynamics for Unknown Hyperbolic Conservation Laws Using Deep Neural Networks","display_name":"Learning the Dynamics for Unknown Hyperbolic Conservation Laws Using Deep Neural Networks","publication_year":2024,"publication_date":"2024-03-06","ids":{"openalex":"https://openalex.org/W4392517081","doi":"https://doi.org/10.1137/22m1537333"},"language":"en","primary_location":{"id":"doi:10.1137/22m1537333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1537333","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/A5013433350","display_name":"Zhen Chen","orcid":"https://orcid.org/0000-0002-9412-9774"},"institutions":[{"id":"https://openalex.org/I923382979","display_name":"ExxonMobil (United States)","ror":"https://ror.org/01xcepn55","country_code":"US","type":"company","lineage":["https://openalex.org/I923382979"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhen Chen","raw_affiliation_strings":["ExxonMobil Technology and Engineering Company, Spring, TX 77389 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ExxonMobil Technology and Engineering Company, Spring, TX 77389 USA","institution_ids":["https://openalex.org/I923382979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052474931","display_name":"Anne Gelb","orcid":"https://orcid.org/0000-0002-9219-4572"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anne Gelb","raw_affiliation_strings":["Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA"],"raw_orcid":"https://orcid.org/0000-0002-9219-4572","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069968312","display_name":"Yoonsang Lee","orcid":"https://orcid.org/0000-0002-5573-9414"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yoonsang Lee","raw_affiliation_strings":["Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013433350"],"corresponding_institution_ids":["https://openalex.org/I923382979"],"apc_list":null,"apc_paid":null,"fwci":2.1566,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86747043,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"A825","last_page":"A850"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9958999752998352,"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/T12560","display_name":"Nuclear Engineering Thermal-Hydraulics","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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":0.8591933250427246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.763960599899292},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.544783890247345},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.51189124584198},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4759090542793274},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3205227851867676},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2891758382320404},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17288526892662048}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8591933250427246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763960599899292},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.544783890247345},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.51189124584198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4759090542793274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3205227851867676},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2891758382320404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17288526892662048},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1537333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1537333","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":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G235927026","display_name":null,"funder_award_id":"DMS 1912685","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6422990862","display_name":null,"funder_award_id":"ONR N00014-20-1-2595","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G7908044143","display_name":null,"funder_award_id":"DMS 1912999","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8835246351","display_name":null,"funder_award_id":"FA9550-22-1-0411","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1555627060","https://openalex.org/W1969647398","https://openalex.org/W2005490094","https://openalex.org/W2009447971","https://openalex.org/W2034976587","https://openalex.org/W2111406701","https://openalex.org/W2124138287","https://openalex.org/W2239232218","https://openalex.org/W2525748878","https://openalex.org/W2782116534","https://openalex.org/W2899283552","https://openalex.org/W2919115771","https://openalex.org/W2951629468","https://openalex.org/W2962957385","https://openalex.org/W2966473221","https://openalex.org/W2979786244","https://openalex.org/W2980396542","https://openalex.org/W2997405608","https://openalex.org/W3000947656","https://openalex.org/W3004857598","https://openalex.org/W3005071597","https://openalex.org/W3010292040","https://openalex.org/W3015865829","https://openalex.org/W3026669735","https://openalex.org/W3094231958","https://openalex.org/W3144086130","https://openalex.org/W3158172875","https://openalex.org/W3163993681","https://openalex.org/W3198730848","https://openalex.org/W3205265842","https://openalex.org/W3217247658","https://openalex.org/W4229368245","https://openalex.org/W4297094032","https://openalex.org/W4307046645"],"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":{".We":[0],"propose":[1],"a":[2,32,70],"new":[3,33],"data-driven":[4],"method":[5],"to":[6,43,82,110],"learn":[7],"the":[8,40,45,50,58,90,94,104],"dynamics":[9],"of":[10,15,49],"an":[11],"unknown":[12,51],"hyperbolic":[13],"system":[14],"conservation":[16,28],"laws":[17],"using":[18,69,89],"deep":[19],"neural":[20],"networks.":[21],"Inspired":[22],"by":[23],"classical":[24],"methods":[25],"in":[26,38],"numerical":[27,46,54],"laws,":[29],"we":[30],"develop":[31],"conservative":[34],"form":[35,73,119],"network":[36,41],"(CFN)":[37],"which":[39],"learns":[42],"approximate":[44],"flux":[47],"function":[48],"system.":[52],"Our":[53],"examples":[55],"demonstrate":[56],"that":[57],"CFN":[59,91],"yields":[60],"significantly":[61],"better":[62],"prediction":[63],"accuracy":[64],"than":[65],"what":[66],"is":[67,78],"obtained":[68,88],"standard":[71],"nonconservative":[72],"network,":[74],"even":[75],"when":[76],"it":[77],"enhanced":[79],"with":[80],"constraints":[81],"promote":[83],"conservation.":[84],"In":[85],"particular,":[86],"solutions":[87],"consistently":[92],"capture":[93],"correct":[95],"shock":[96],"propagation":[97],"speed":[98],"without":[99],"introducing":[100],"nonphysical":[101],"oscillations":[102],"into":[103],"solution.":[105],"They":[106],"are":[107],"furthermore":[108],"robust":[109],"noisy":[111],"and":[112],"sparse":[113],"observation":[114],"environments.Keywordsconservation":[115],"lawsdata-driven":[116],"methodneural":[117],"networksconservative":[118],"networkMSC":[120],"codes65M1235L6562M45":[121]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}