{"id":"https://openalex.org/W3022657828","doi":"https://doi.org/10.3934/nhm.2020011","title":"Deep neural network approach to forward-inverse problems","display_name":"Deep neural network approach to forward-inverse problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3022657828","doi":"https://doi.org/10.3934/nhm.2020011","mag":"3022657828"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2020011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2020011","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2020011","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062562218","display_name":"Hyeontae Jo","orcid":"https://orcid.org/0000-0003-4637-8722"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hyeontae Jo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045120821","display_name":"Hwijae Son","orcid":"https://orcid.org/0000-0002-6630-2832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hwijae Son","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003733262","display_name":"Hyung Ju Hwang","orcid":"https://orcid.org/0000-0002-3678-2687"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hyung Ju Hwang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111451369","display_name":"Eun Heui Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eun Heui Kim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062562218"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4001,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.8876715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"247","last_page":"259"},"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/T11052","display_name":"Energy Load and Power Forecasting","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6224355697631836},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6170138120651245},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5152568817138672},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5099519491195679},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49163728952407837},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.4487732946872711},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.42023104429244995},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.4196363389492035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4095470905303955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3964040279388428},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33852142095565796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2822885513305664},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23665904998779297},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10075724124908447}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6224355697631836},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6170138120651245},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5152568817138672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5099519491195679},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49163728952407837},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.4487732946872711},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.42023104429244995},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.4196363389492035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4095470905303955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3964040279388428},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33852142095565796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2822885513305664},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23665904998779297},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10075724124908447},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2020011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2020011","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6bb3cd0af93247c880def64b9b063c1f","is_oa":false,"landing_page_url":"https://doaj.org/article/6bb3cd0af93247c880def64b9b063c1f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 15, Iss 2, Pp 247-259 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2020011","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2020011","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1522301498","https://openalex.org/W2779338154","https://openalex.org/W2951651062"],"related_works":["https://openalex.org/W2103147384","https://openalex.org/W2152280668","https://openalex.org/W2339811963","https://openalex.org/W2078520445","https://openalex.org/W4320858067","https://openalex.org/W2388390852","https://openalex.org/W4281994489","https://openalex.org/W4379261276","https://openalex.org/W3131897592","https://openalex.org/W4379924588"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>In":[1],"this":[2],"paper,":[3],"we":[4,19,39,108],"construct":[5],"approximated":[6],"solutions":[7],"of":[8,27,44,60,78,116],"Differential":[9],"Equations":[10],"(DEs)":[11],"using":[12],"the":[13,25,34,90,114,132],"Deep":[14],"Neural":[15],"Network":[16],"(DNN).":[17],"Furthermore,":[18],"present":[20],"an":[21,49,96],"architecture":[22,46,58,120],"that":[23,47,89],"includes":[24],"process":[26],"finding":[28],"model":[29,54],"parameters":[30,55],"through":[31],"experimental":[32],"data,":[33],"inverse":[35],"problem.":[36],"That":[37],"is,":[38],"provide":[40],"a":[41,61,100],"unified":[42],"framework":[43],"DNN":[45,64,92,119],"approximates":[48],"analytic":[50,97],"solution":[51,93,98],"and":[52,80,131],"its":[53],"simultaneously.":[56],"The":[57],"consists":[59],"feed":[62],"forward":[63],"with":[65],"non-linear":[66],"activation":[67],"functions":[68],"depending":[69],"on":[70],"DEs,":[71],"automatic":[72],"differentiation":[73],"[<xref":[74],"ref-type=\"bibr\"":[75],"rid=\"b2\">2</xref>],":[76],"reduction":[77],"order,":[79],"gradient":[81],"based":[82],"optimization":[83],"method.":[84],"We":[85],"also":[86],"prove":[87],"theoretically":[88],"proposed":[91],"converges":[94],"to":[95,112],"in":[99],"suitable":[101],"function":[102],"space":[103],"for":[104,121],"fundamental":[105],"DEs.":[106],"Finally,":[107],"perform":[109],"numerical":[110],"experiments":[111],"validate":[113],"robustness":[115],"our":[117],"simplistic":[118],"1D":[122],"transport":[123],"equation,":[124,127,130],"2D":[125,128],"heat":[126],"wave":[129],"Lotka-Volterra":[133],"system.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}