{"id":"https://openalex.org/W4399574644","doi":"https://doi.org/10.1016/j.cpc.2024.109275","title":"Decoupling numerical method based on deep neural network for nonlinear degenerate interface problems","display_name":"Decoupling numerical method based on deep neural network for nonlinear degenerate interface problems","publication_year":2024,"publication_date":"2024-06-12","ids":{"openalex":"https://openalex.org/W4399574644","doi":"https://doi.org/10.1016/j.cpc.2024.109275"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cpc.2024.109275","pdf_url":null,"source":{"id":"https://openalex.org/S142305363","display_name":"Computer Physics Communications","issn_l":"0010-4655","issn":["0010-4655","1879-2944"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2306.02266","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100322088","display_name":"Fan Chen","orcid":"https://orcid.org/0000-0002-5986-1708"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Fan","raw_affiliation_strings":["School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012082265","display_name":"Muhammad Aamir Ali","orcid":"https://orcid.org/0000-0001-5341-4926"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Muhammad Aamir Ali","raw_affiliation_strings":["School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038705826","display_name":"Zhiyue Zhang","orcid":"https://orcid.org/0000-0001-7070-2532"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiyue Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing 210023, China","institution_ids":["https://openalex.org/I152031979"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038705826"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"apc_list":{"value":3670,"currency":"USD","value_usd":3670,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":85,"max":94},"biblio":{"volume":"303","issue":null,"first_page":"109275","last_page":"109275"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Finite Element Methods for Fluid-Structure Interaction","score":0.9998,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Finite Element Methods for Fluid-Structure Interaction","score":0.9998,"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/T11206","display_name":"Physics-Informed Neural Networks for Scientific Computing","score":0.9985,"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/T10514","display_name":"Fracture Mechanics Modeling and Simulation","score":0.9981,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/decoupling","display_name":"Decoupling (probability)","score":0.5631607},{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic Mode Decomposition","score":0.549285},{"id":"https://openalex.org/keywords/nonlinear-systems","display_name":"Nonlinear Systems","score":0.532841},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5300241},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep Learning","score":0.529333},{"id":"https://openalex.org/keywords/numerical-computing","display_name":"Numerical Computing","score":0.527478},{"id":"https://openalex.org/keywords/model-reduction","display_name":"Model Reduction","score":0.517018}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6340141},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.62841386},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5631607},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.53431475},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5300241},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5035772},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.499326},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48999324},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.48223957},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45946503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45337033},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.43185514},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.391682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34799138},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3163598},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0986242},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09167418},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"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/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cpc.2024.109275","pdf_url":null,"source":{"id":"https://openalex.org/S142305363","display_name":"Computer Physics Communications","issn_l":"0010-4655","issn":["0010-4655","1879-2944"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2306.02266","pdf_url":"https://arxiv.org/pdf/2306.02266","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2306.02266","pdf_url":"https://arxiv.org/pdf/2306.02266","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"11971241"}],"datasets":[],"versions":[],"referenced_works_count":62,"referenced_works":["https://openalex.org/W1525628435","https://openalex.org/W1541274513","https://openalex.org/W1974936486","https://openalex.org/W1977856502","https://openalex.org/W1994616650","https://openalex.org/W1997612340","https://openalex.org/W2006446053","https://openalex.org/W2014475794","https://openalex.org/W2028127312","https://openalex.org/W2029529153","https://openalex.org/W2042669113","https://openalex.org/W2042921302","https://openalex.org/W2058436955","https://openalex.org/W2065588867","https://openalex.org/W2070135540","https://openalex.org/W2092265656","https://openalex.org/W2093012115","https://openalex.org/W2095548561","https://openalex.org/W2098171572","https://openalex.org/W2114405526","https://openalex.org/W2114589706","https://openalex.org/W2119611099","https://openalex.org/W2127907812","https://openalex.org/W2141613219","https://openalex.org/W2158985775","https://openalex.org/W2168806188","https://openalex.org/W2507089618","https://openalex.org/W2520200476","https://openalex.org/W2528305538","https://openalex.org/W2586353034","https://openalex.org/W2589552012","https://openalex.org/W269348287","https://openalex.org/W2760972773","https://openalex.org/W2790914254","https://openalex.org/W2899399074","https://openalex.org/W2908429425","https://openalex.org/W2912777423","https://openalex.org/W2913668833","https://openalex.org/W2919115771","https://openalex.org/W2962974623","https://openalex.org/W2963397265","https://openalex.org/W2990234860","https://openalex.org/W2991946954","https://openalex.org/W3022977644","https://openalex.org/W3093786597","https://openalex.org/W3098172061","https://openalex.org/W3099661895","https://openalex.org/W3102629495","https://openalex.org/W3105662320","https://openalex.org/W3111767734","https://openalex.org/W3112182983","https://openalex.org/W3121554115","https://openalex.org/W3123381822","https://openalex.org/W3130605572","https://openalex.org/W3143309364","https://openalex.org/W3156054739","https://openalex.org/W3176116059","https://openalex.org/W3186608048","https://openalex.org/W3190928351","https://openalex.org/W3194468165","https://openalex.org/W4294958351","https://openalex.org/W4362508031"],"related_works":["https://openalex.org/W4302011306","https://openalex.org/W4287265842","https://openalex.org/W2963052782","https://openalex.org/W2726339783","https://openalex.org/W2546079289","https://openalex.org/W2148110192","https://openalex.org/W2095039895","https://openalex.org/W2077972311","https://openalex.org/W2022448890","https://openalex.org/W2022135995"],"abstract_inverted_index":{"Many":[0],"practical":[1],"problems,":[2],"including":[3,228],"modeling":[4],"composite":[5],"materials,":[6],"nuclear":[7],"waste":[8],"disposal,":[9],"oil":[10],"reservoir":[11],"simulations,":[12],"and":[13,78,97,117,169,230,240,246,265],"flows":[14],"in":[15],"porous":[16],"medium,":[17],"commonly":[18],"involve":[19],"interface":[20,26,47,65,141,204,226,261],"problems.":[21,248],"However,":[22],"the":[23,46,73,84,91,94,99,102,106,113,128,155,158,161,188,197,202,207,225,238,254,260],"solution":[24,92,100,159],"to":[25,44,89,127,132],"problems":[27,48,66,147,174,205,227,262],"with":[28,49,67,139,178,234,263,271],"discontinuous":[29],"coefficients":[30],"of":[31,115,157,187,199,201,242],"PDEs":[32],"using":[33,105],"fully":[34,50],"decoupled":[35,51,59],"numerical":[36,52,60,182],"methods":[37,243],"is":[38,43,121,131,191,250,257],"challenging.":[39],"The":[40,110,125,184],"main":[41,185],"objective":[42],"solve":[45],"methods.":[53,183],"This":[54],"paper":[55],"proposes":[56],"an":[57,122,140],"efficient":[58],"method":[61,256],"for":[62,224,244,259],"solving":[63],"degenerate":[64,135,203,229,264],"double":[68],"singularities.":[69],"First,":[70],"we":[71,82,193,211,236,268],"divide":[72],"whole":[74,208],"domain":[75,163],"into":[76,142],"singular":[77,95,116,162],"regular":[79,103,118],"subdomains.":[80],"Then,":[81],"use":[83],"Deep":[85],"Neural":[86],"Network":[87],"(DNN)":[88],"find":[90],"on":[93,101,149,160,206],"subdomain":[96,104],"approximate":[98],"finite":[107],"difference":[108],"method.":[109],"scheme":[111,190],"combines":[112],"solutions":[114],"subdomains,":[119],"which":[120],"exciting":[123],"idea.":[124],"key":[126],"new":[129],"approach":[130],"split":[133],"nonlinear":[134],"partial":[136],"differential":[137],"equations":[138],"two":[143,170],"independent":[144,171],"boundary":[145,172],"value":[146,173],"based":[148],"deep":[150],"learning.":[151],"In":[152],"this":[153],"way,":[154],"expansion":[156],"does":[164],"not":[165,194],"contain":[166],"undetermined":[167],"parameters,":[168],"can":[175,213],"be":[176],"solved":[177],"any":[179],"well-known":[180],"traditional":[181],"advantage":[186],"proposed":[189,255],"that":[192,253],"only":[195],"get":[196],"order":[198],"convergence":[200],"domain,":[209],"but":[210],"also":[212,251],"calculate":[214],"VERY":[215],"BIG":[216],"jump":[217],"ratio":[218],"(such":[219],"as":[220],"1012:1":[221],"or":[222],"1:1012)":[223],"non-degenerate":[231,266],"cases.":[232],"Finally,":[233],"examples,":[235],"demonstrate":[237],"efficiency":[239],"accuracy":[241],"1":[245],"2D":[247],"It":[249],"interesting":[252],"valid":[258],"cases,":[267],"show":[269],"it":[270],"some":[272],"examples.":[273]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4399574644","counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2024-11-27T13:59:10.525617","created_date":"2024-06-13"}