{"id":"https://openalex.org/W2890443329","doi":"https://doi.org/10.1007/s11063-018-9911-8","title":"Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm","display_name":"Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm","publication_year":2018,"publication_date":"2018-09-05","ids":{"openalex":"https://openalex.org/W2890443329","doi":"https://doi.org/10.1007/s11063-018-9911-8","mag":"2890443329"},"language":"en","primary_location":{"id":"doi:10.1007/s11063-018-9911-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11063-018-9911-8","pdf_url":null,"source":{"id":"https://openalex.org/S140962798","display_name":"Neural Processing Letters","issn_l":"1370-4621","issn":["1370-4621","1573-773X"],"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":"Neural Processing Letters","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/A5018635068","display_name":"Hongli Sun","orcid":"https://orcid.org/0000-0002-0360-6695"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongli Sun","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047660471","display_name":"Muzhou Hou","orcid":"https://orcid.org/0000-0001-6658-2187"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Muzhou Hou","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, 410083, China"],"raw_orcid":"https://orcid.org/0000-0001-6658-2187","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101047123","display_name":"Yunlei Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunlei Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059107732","display_name":"Tianle Zhang","orcid":"https://orcid.org/0000-0003-4881-2406"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianle Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066491071","display_name":"Futian Weng","orcid":"https://orcid.org/0000-0002-7982-8729"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Futian Weng","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, 410083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, 410083, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060208182","display_name":"Feng Han","orcid":"https://orcid.org/0000-0002-3411-5573"},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Han","raw_affiliation_strings":["College of Science, Hunan University of Technology, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hunan University of Technology, Hunan, China","institution_ids":["https://openalex.org/I49934816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5047660471"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.927,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.97468634,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"50","issue":"2","first_page":"1153","last_page":"1172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9998000264167786,"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/T10320","display_name":"Neural Networks and Applications","score":0.9962999820709229,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/extreme-learning-machine","display_name":"Extreme learning machine","score":0.7436115145683289},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7104794383049011},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.6957907676696777},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6565961241722107},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6414949297904968},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.5857439041137695},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.5165623426437378},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49925684928894043},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.47754204273223877},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.4136888086795807},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34412243962287903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25849449634552},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2344871163368225}],"concepts":[{"id":"https://openalex.org/C2780150128","wikidata":"https://www.wikidata.org/wiki/Q21948731","display_name":"Extreme learning machine","level":3,"score":0.7436115145683289},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7104794383049011},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.6957907676696777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6565961241722107},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6414949297904968},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.5857439041137695},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.5165623426437378},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49925684928894043},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.47754204273223877},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.4136888086795807},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34412243962287903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25849449634552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2344871163368225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11063-018-9911-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11063-018-9911-8","pdf_url":null,"source":{"id":"https://openalex.org/S140962798","display_name":"Neural Processing Letters","issn_l":"1370-4621","issn":["1370-4621","1573-773X"],"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":"Neural Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1530216100","display_name":null,"funder_award_id":"61375063","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"},{"id":"https://openalex.org/F4320321514","display_name":"Central South University","ror":"https://ror.org/00f1zfq44"},{"id":"https://openalex.org/F4320322191","display_name":"Hunan University","ror":"https://ror.org/05htk5m33"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1512069430","https://openalex.org/W1535382688","https://openalex.org/W1634261337","https://openalex.org/W1966820249","https://openalex.org/W1972567945","https://openalex.org/W1979461565","https://openalex.org/W1980697694","https://openalex.org/W1987618706","https://openalex.org/W1990028209","https://openalex.org/W2000737269","https://openalex.org/W2006410600","https://openalex.org/W2006610075","https://openalex.org/W2008007187","https://openalex.org/W2011382171","https://openalex.org/W2020561998","https://openalex.org/W2024562774","https://openalex.org/W2026656818","https://openalex.org/W2028882710","https://openalex.org/W2031849203","https://openalex.org/W2035666253","https://openalex.org/W2044507389","https://openalex.org/W2055896346","https://openalex.org/W2062503449","https://openalex.org/W2067485895","https://openalex.org/W2068289155","https://openalex.org/W2068616545","https://openalex.org/W2111072639","https://openalex.org/W2132473313","https://openalex.org/W2134201856","https://openalex.org/W2135791206","https://openalex.org/W2142321415","https://openalex.org/W2144584868","https://openalex.org/W2148666448","https://openalex.org/W2150665357","https://openalex.org/W2154718502","https://openalex.org/W2157599435","https://openalex.org/W2158985775","https://openalex.org/W2164004695","https://openalex.org/W2275233666","https://openalex.org/W2520751857","https://openalex.org/W2727042597","https://openalex.org/W2732497708","https://openalex.org/W2757176621","https://openalex.org/W2784350881","https://openalex.org/W2803225469","https://openalex.org/W3101260193"],"related_works":["https://openalex.org/W2067443264","https://openalex.org/W31566076","https://openalex.org/W4297902562","https://openalex.org/W2741186499","https://openalex.org/W2804652951","https://openalex.org/W2968645206","https://openalex.org/W2556335056","https://openalex.org/W2002678693","https://openalex.org/W1993717606","https://openalex.org/W2029287765"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
