{"id":"https://openalex.org/W2922646101","doi":"https://doi.org/10.1007/s00500-019-03944-1","title":"Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations","display_name":"Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations","publication_year":2019,"publication_date":"2019-03-26","ids":{"openalex":"https://openalex.org/W2922646101","doi":"https://doi.org/10.1007/s00500-019-03944-1","mag":"2922646101"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-019-03944-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-019-03944-1","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"Soft 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/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/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/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/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/A5101514215","display_name":"Jianshu Luo","orcid":"https://orcid.org/0000-0002-1421-6406"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianshu Luo","raw_affiliation_strings":["College of Science, National University of Defense Technology, Changsha, 410073, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, National University of Defense Technology, Changsha, 410073, China","institution_ids":["https://openalex.org/I170215575"]}]}],"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":4.6275,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.9574315,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"24","issue":"2","first_page":"1083","last_page":"1096"},"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/T11277","display_name":"Thermal properties of materials","score":0.9668999910354614,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9656000137329102,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8124270439147949},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7063528895378113},{"id":"https://openalex.org/keywords/extreme-learning-machine","display_name":"Extreme learning machine","score":0.6485341787338257},{"id":"https://openalex.org/keywords/legendre-wavelet","display_name":"Legendre wavelet","score":0.5012030601501465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49504485726356506},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4829210937023163},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48145169019699097},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.47115838527679443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4323383867740631},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20916584134101868},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10565811395645142}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8124270439147949},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7063528895378113},{"id":"https://openalex.org/C2780150128","wikidata":"https://www.wikidata.org/wiki/Q21948731","display_name":"Extreme learning machine","level":3,"score":0.6485341787338257},{"id":"https://openalex.org/C123769847","wikidata":"https://www.wikidata.org/wiki/Q6517888","display_name":"Legendre wavelet","level":5,"score":0.5012030601501465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49504485726356506},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4829210937023163},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48145169019699097},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.47115838527679443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4323383867740631},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20916584134101868},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10565811395645142},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00500-019-03944-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-019-03944-1","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"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":"Soft Computing","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W597024874","https://openalex.org/W1634261337","https://openalex.org/W1915329794","https://openalex.org/W1968064923","https://openalex.org/W1990938413","https://openalex.org/W2002011878","https://openalex.org/W2003733968","https://openalex.org/W2006610075","https://openalex.org/W2015788898","https://openalex.org/W2026131661","https://openalex.org/W2026656818","https://openalex.org/W2036130869","https://openalex.org/W2042403004","https://openalex.org/W2049106450","https://openalex.org/W2057098763","https://openalex.org/W2057377888","https://openalex.org/W2059548105","https://openalex.org/W2065541244","https://openalex.org/W2070851600","https://openalex.org/W2073267518","https://openalex.org/W2073365653","https://openalex.org/W2082609151","https://openalex.org/W2085496778","https://openalex.org/W2092950528","https://openalex.org/W2102871258","https://openalex.org/W2111072639","https://openalex.org/W2113062149","https://openalex.org/W2122040390","https://openalex.org/W2124776405","https://openalex.org/W2141695047","https://openalex.org/W2154621583","https://openalex.org/W2158985775","https://openalex.org/W2219232438","https://openalex.org/W2279039799","https://openalex.org/W2351844501","https://openalex.org/W2520751857","https://openalex.org/W2542993152","https://openalex.org/W2544492256","https://openalex.org/W2552309921","https://openalex.org/W2554616561","https://openalex.org/W2563167163","https://openalex.org/W2580977989","https://openalex.org/W2622634640","https://openalex.org/W2770344288","https://openalex.org/W2799501716","https://openalex.org/W2800070384","https://openalex.org/W2890443329","https://openalex.org/W2890970224","https://openalex.org/W2901941709","https://openalex.org/W2915062141","https://openalex.org/W3101260193","https://openalex.org/W3125537303","https://openalex.org/W3146026292"],"related_works":["https://openalex.org/W2545227774","https://openalex.org/W2259159807","https://openalex.org/W3130851271","https://openalex.org/W2788092364","https://openalex.org/W4313180762","https://openalex.org/W2385225694","https://openalex.org/W2357310454","https://openalex.org/W1607269076","https://openalex.org/W2343666563","https://openalex.org/W2612851455"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}