{"id":"https://openalex.org/W3088619209","doi":"https://doi.org/10.1007/s10915-022-01930-8","title":"The Deep Learning Galerkin Method for the General Stokes Equations","display_name":"The Deep Learning Galerkin Method for the General Stokes Equations","publication_year":2022,"publication_date":"2022-08-22","ids":{"openalex":"https://openalex.org/W3088619209","doi":"https://doi.org/10.1007/s10915-022-01930-8","mag":"3088619209"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-022-01930-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-022-01930-8","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of 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/A5100402579","display_name":"Jian Li","orcid":"https://orcid.org/0000-0003-1357-3089"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jian Li","raw_affiliation_strings":["School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi\u2019an, China","School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101403207","display_name":"Jing Yue","orcid":"https://orcid.org/0000-0002-8936-0162"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Yue","raw_affiliation_strings":["School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi\u2019an, China","School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi'an, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024516353","display_name":"Zhang Wen","orcid":"https://orcid.org/0000-0001-9672-3219"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Zhang","raw_affiliation_strings":["School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi\u2019an, China","School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi\u2019an, China","institution_ids":["https://openalex.org/I51622183"]},{"raw_affiliation_string":"School of Electrical and Control Engineering, Shaanxi University of Science and Technology, Xi'an, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023933852","display_name":"Wansuo Duan","orcid":"https://orcid.org/0000-0002-0122-2794"},"institutions":[{"id":"https://openalex.org/I4210152758","display_name":"Institute of Atmospheric Physics","ror":"https://ror.org/0424h4e32","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210152758"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wansuo Duan","raw_affiliation_strings":["Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210152758","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100402579"],"corresponding_institution_ids":["https://openalex.org/I51622183"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.7514,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.84064199,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"93","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.7017649412155151},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.685350239276886},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6273404955863953},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5275114178657532},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49309441447257996},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47954699397087097},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4728665053844452},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46701934933662415},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3744339048862457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37053319811820984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2639557719230652},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2487674355506897},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19217947125434875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7017649412155151},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.685350239276886},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6273404955863953},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5275114178657532},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49309441447257996},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47954699397087097},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4728665053844452},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46701934933662415},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3744339048862457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37053319811820984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2639557719230652},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2487674355506897},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19217947125434875},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-022-01930-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-022-01930-8","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5367029097","display_name":null,"funder_award_id":"11771259","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1512069430","https://openalex.org/W1866311589","https://openalex.org/W1988115241","https://openalex.org/W2018535469","https://openalex.org/W2090799250","https://openalex.org/W2142321415","https://openalex.org/W2143163345","https://openalex.org/W2158985775","https://openalex.org/W2520751857","https://openalex.org/W2550039210","https://openalex.org/W2749028154","https://openalex.org/W2770250658","https://openalex.org/W2772097715","https://openalex.org/W2784733489","https://openalex.org/W2787240879","https://openalex.org/W2797393904","https://openalex.org/W2890443329","https://openalex.org/W2899283552","https://openalex.org/W2908541468","https://openalex.org/W2912649832","https://openalex.org/W2969381807","https://openalex.org/W2997588930","https://openalex.org/W3002919193","https://openalex.org/W3009483635","https://openalex.org/W3010849941","https://openalex.org/W3025593802","https://openalex.org/W3045625682","https://openalex.org/W3093786597","https://openalex.org/W3101260193","https://openalex.org/W3152256596","https://openalex.org/W3164032021","https://openalex.org/W4206719739","https://openalex.org/W4224022852","https://openalex.org/W6601048702"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W4388145910","https://openalex.org/W1976205134","https://openalex.org/W2381570729","https://openalex.org/W4248336175","https://openalex.org/W3009369890","https://openalex.org/W2031260042","https://openalex.org/W2391445434","https://openalex.org/W4312490297","https://openalex.org/W2062212388"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}