{"id":"https://openalex.org/W4388486456","doi":"https://doi.org/10.1109/access.2023.3331330","title":"A Solution Method for Differential Equations Based on Taylor PINN","display_name":"A Solution Method for Differential Equations Based on Taylor PINN","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4388486456","doi":"https://doi.org/10.1109/access.2023.3331330"},"language":"en","primary_location":{"id":"doi:10.1109/access.2023.3331330","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3331330","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10311559.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10311559.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100687628","display_name":"Yajuan Zhang","orcid":"https://orcid.org/0000-0003-0783-4836"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yajuan Zhang","raw_affiliation_strings":["College of Information Engineering, Hainan Vocational University of Science and Technology, Haikou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Engineering, Hainan Vocational University of Science and Technology, Haikou, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009851741","display_name":"M Y Wang","orcid":"https://orcid.org/0009-0004-3390-9525"},"institutions":[{"id":"https://openalex.org/I4210099312","display_name":"Shandong Jiaotong University","ror":"https://ror.org/01848hk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Wang","raw_affiliation_strings":["Department of Basic Education, Shandong Jiaotong University, Weihai, China","Department of Basic Education, Shandong Jiaotong University, Weihai, Shandong, China"],"raw_orcid":"https://orcid.org/0009-0004-3390-9525","affiliations":[{"raw_affiliation_string":"Department of Basic Education, Shandong Jiaotong University, Weihai, China","institution_ids":["https://openalex.org/I4210099312"]},{"raw_affiliation_string":"Department of Basic Education, Shandong Jiaotong University, Weihai, Shandong, China","institution_ids":["https://openalex.org/I4210099312"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079150616","display_name":"Fangwei Zhang","orcid":"https://orcid.org/0000-0003-1511-2155"},"institutions":[{"id":"https://openalex.org/I4210099312","display_name":"Shandong Jiaotong University","ror":"https://ror.org/01848hk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fangwei Zhang","raw_affiliation_strings":["School of Maritime, Shandong Jiaotong University, Weihai, China","School of Maritime, Shandong Jiaotong University, Weihai, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Maritime, Shandong Jiaotong University, Weihai, China","institution_ids":["https://openalex.org/I4210099312"]},{"raw_affiliation_string":"School of Maritime, Shandong Jiaotong University, Weihai, Shandong, China","institution_ids":["https://openalex.org/I4210099312"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103091111","display_name":"Zhenrui Chen","orcid":"https://orcid.org/0000-0002-6521-3459"},"institutions":[{"id":"https://openalex.org/I4210099312","display_name":"Shandong Jiaotong University","ror":"https://ror.org/01848hk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099312"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenrui Chen","raw_affiliation_strings":["Department of Basic Education, Shandong Jiaotong University, Weihai, China","Department of Basic Education, Shandong Jiaotong University, Weihai, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Education, Shandong Jiaotong University, Weihai, China","institution_ids":["https://openalex.org/I4210099312"]},{"raw_affiliation_string":"Department of Basic Education, Shandong Jiaotong University, Weihai, Shandong, China","institution_ids":["https://openalex.org/I4210099312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100687628"],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":1.2795,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78941716,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":null,"first_page":"145020","last_page":"145030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9937999844551086,"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":0.9937999844551086,"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/T10320","display_name":"Neural Networks and Applications","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13286","display_name":"Modeling and Simulation Systems","score":0.9417999982833862,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5369017124176025},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4765266180038452},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46783486008644104},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4427056908607483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3643419146537781},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3001340627670288}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5369017124176025},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4765266180038452},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46783486008644104},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4427056908607483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3643419146537781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3001340627670288}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2023.3331330","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3331330","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10311559.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9ef59de2110c4dc1a3826b2a5b0c8355","is_oa":true,"landing_page_url":"https://doaj.org/article/9ef59de2110c4dc1a3826b2a5b0c8355","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 11, Pp 145020-145030 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2023.3331330","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2023.3331330","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/10311559.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322866","display_name":"Natural Science Foundation of Hainan Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325569","display_name":"Shandong Jiaotong University","ror":"https://ror.org/01848hk04"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388486456.pdf","grobid_xml":"https://content.openalex.org/works/W4388486456.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W2034903716","https://openalex.org/W2770250658","https://openalex.org/W2792564469","https://openalex.org/W2907294897","https://openalex.org/W2912149013","https://openalex.org/W2952550171","https://openalex.org/W2963378054","https://openalex.org/W3011031911","https://openalex.org/W3015647587","https://openalex.org/W3027712952","https://openalex.org/W3036567110","https://openalex.org/W3043050416","https://openalex.org/W3083828368","https://openalex.org/W3087644732","https://openalex.org/W3104183394","https://openalex.org/W3106489632","https://openalex.org/W3133363975","https://openalex.org/W3149510846","https://openalex.org/W3173031848","https://openalex.org/W3196379841","https://openalex.org/W4214506712","https://openalex.org/W4229368245","https://openalex.org/W4288276633","https://openalex.org/W6752307458","https://openalex.org/W6762981976","https://openalex.org/W6766280392","https://openalex.org/W6774132597","https://openalex.org/W6778353478","https://openalex.org/W6783678127","https://openalex.org/W6785328185","https://openalex.org/W6793606235","https://openalex.org/W6796224952"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W1984106009","https://openalex.org/W1815130818"],"abstract_inverted_index":{"Based":[0],"on":[1,128,167],"deep":[2,30,129,145],"neural":[3,33,59,68,87,97,130,146,216],"network,":[4,34],"elliptic":[5,22,46],"partial":[6,23,47,101,110,122],"differential":[7,24,48,102,111,123],"equations":[8,25,174],"in":[9,191],"complex":[10],"regions":[11],"are":[12,26,40],"solved.":[13],"Accurate":[14],"and":[15,18,77,148,171,195],"effective":[16],"strategies":[17],"numerical":[19,160,164,206,229],"methods":[20],"for":[21,227],"proposed":[27],"by":[28,52,224],"implementing":[29],"feedforward":[31],"artificial":[32],"appropriate":[35],"loss":[36],"function":[37,67,74,86,96,150],"solving":[38,109,125],"strategy":[39],"constructed.":[41],"The":[42,163],"solution":[43,161],"of":[44,57,80,108,115,144,153,188,198],"an":[45],"equation":[49,124],"is":[50,118],"obtained":[51],"iteratively":[53],"learning":[54],"the":[55,72,81,113,140,149,182,186,192,196,199],"parameters":[56],"a":[58,62,158],"network.":[60,88],"Constructing":[61],"composite":[63,92],"multi-layer":[64,83,93],"radial":[65,84,94],"basis":[66,85,95],"network":[69,98,217],"can":[70,179,203],"improve":[71],"real":[73],"approximation":[75,142],"performance":[76],"operational":[78],"accuracy":[79,223],"constructed":[82],"Use":[89],"this":[90,116],"high-precision":[91],"to":[99,156],"solve":[100],"equations.":[103],"By":[104],"providing":[105],"specific":[106],"examples":[107],"equations,":[112],"effectiveness":[114],"method":[117,126,138],"tested.":[119],"An":[120],"improved":[121],"based":[127,215],"networks":[131,147],"(Taylor":[132],"PINN)":[133],"has":[134],"been":[135],"proposed.":[136],"This":[137],"utilizes":[139],"universal":[141],"theorem":[143],"fitting":[151],"ability":[152],"Taylor\u2019s":[154],"formula":[155],"achieve":[157],"meshless":[159],"process.":[162],"experimental":[165],"results":[166],"Helmholtz,":[168],"Klein":[169],"Gordon,":[170],"Navier":[172],"Stokes":[173],"show":[175],"that":[176],"Taylor":[177,219],"PINN":[178,220],"well":[180],"fit":[181],"mapping":[183],"relationship":[184],"between":[185],"coordinates":[187],"spatiotemporal":[189],"points":[190],"computational":[193],"domain":[194],"value":[197],"desired":[200],"function,":[201],"which":[202],"provide":[204],"accurate":[205],"prediction":[207,222],"results.":[208],"Compared":[209],"with":[210],"commonly":[211],"used":[212],"physical":[213],"information":[214],"methods,":[218],"improves":[221],"3-20":[225],"times":[226],"different":[228],"problems.":[230]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
