{"id":"https://openalex.org/W2429563661","doi":"https://doi.org/10.2514/1.i010196","title":"Radial Basis Function Artificial Neural-Network-Inspired Numerical Solver","display_name":"Radial Basis Function Artificial Neural-Network-Inspired Numerical Solver","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2429563661","doi":"https://doi.org/10.2514/1.i010196","mag":"2429563661"},"language":"en","primary_location":{"id":"doi:10.2514/1.i010196","is_oa":false,"landing_page_url":"https://doi.org/10.2514/1.i010196","pdf_url":null,"source":{"id":"https://openalex.org/S4210240151","display_name":"Journal of Aerospace Information Systems","issn_l":"2327-3097","issn":["2327-3097"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315709","host_organization_name":"American Institute of Aeronautics and Astronautics","host_organization_lineage":["https://openalex.org/P4310315709"],"host_organization_lineage_names":["American Institute of Aeronautics and Astronautics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Aerospace Information Systems","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/A5006922544","display_name":"Matthew Wilkinson","orcid":"https://orcid.org/0000-0002-3858-553X"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew C. Wilkinson","raw_affiliation_strings":["Rice University, Houston, Texas 77005"],"affiliations":[{"raw_affiliation_string":"Rice University, Houston, Texas 77005","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082054411","display_name":"Andrew Meade","orcid":"https://orcid.org/0000-0001-7095-7711"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Meade","raw_affiliation_strings":["Rice University, Houston, Texas 77005"],"affiliations":[{"raw_affiliation_string":"Rice University, Houston, Texas 77005","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006922544"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":0.221,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57274641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"13","issue":"6","first_page":"205","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"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":0.9995999932289124,"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/T10514","display_name":"Numerical methods in engineering","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6733171343803406},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.6502417325973511},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6261054277420044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5210144519805908},{"id":"https://openalex.org/keywords/radial-basis-function-network","display_name":"Radial basis function network","score":0.44714343547821045},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3616183400154114},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30981481075286865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2804906964302063}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6733171343803406},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.6502417325973511},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6261054277420044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5210144519805908},{"id":"https://openalex.org/C132917294","wikidata":"https://www.wikidata.org/wiki/Q2679684","display_name":"Radial basis function network","level":4,"score":0.44714343547821045},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3616183400154114},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30981481075286865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2804906964302063}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2514/1.i010196","is_oa":false,"landing_page_url":"https://doi.org/10.2514/1.i010196","pdf_url":null,"source":{"id":"https://openalex.org/S4210240151","display_name":"Journal of Aerospace Information Systems","issn_l":"2327-3097","issn":["2327-3097"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315709","host_organization_name":"American Institute of Aeronautics and Astronautics","host_organization_lineage":["https://openalex.org/P4310315709"],"host_organization_lineage_names":["American Institute of Aeronautics and Astronautics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Aerospace Information Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W395181431","https://openalex.org/W1555627060","https://openalex.org/W1585274809","https://openalex.org/W1609496979","https://openalex.org/W1968270723","https://openalex.org/W1968293773","https://openalex.org/W1987554529","https://openalex.org/W1997027646","https://openalex.org/W2009790961","https://openalex.org/W2013433629","https://openalex.org/W2015628091","https://openalex.org/W2015697821","https://openalex.org/W2027197837","https://openalex.org/W2041858377","https://openalex.org/W2047441604","https://openalex.org/W2047877145","https://openalex.org/W2050067049","https://openalex.org/W2071257506","https://openalex.org/W2071452568","https://openalex.org/W2074976376","https://openalex.org/W2079224763","https://openalex.org/W2080977367","https://openalex.org/W2092011174","https://openalex.org/W2113442785","https://openalex.org/W2121715669","https://openalex.org/W2137983211","https://openalex.org/W2142136198","https://openalex.org/W2145364658","https://openalex.org/W4212943826","https://openalex.org/W4252679991","https://openalex.org/W4297978922","https://openalex.org/W4298060601","https://openalex.org/W4300844655"],"related_works":["https://openalex.org/W130002755","https://openalex.org/W1549106865","https://openalex.org/W1603608513","https://openalex.org/W2393731464","https://openalex.org/W2384647810","https://openalex.org/W2670494184","https://openalex.org/W2375024569","https://openalex.org/W2066360887","https://openalex.org/W1894509194","https://openalex.org/W2348254278"],"abstract_inverted_index":{"A":[0],"framework":[1,72],"for":[2,34,92],"a":[3,48,75],"mesh-free":[4],"numerical":[5],"solver":[6,18],"of":[7,16,47,52,77,86,97,108,124],"differential":[8,54],"equations":[9],"is":[10,19,89,114],"presented":[11,102],"in":[12],"this":[13],"paper.":[14],"Development":[15],"the":[17,45,53,70,83,93,104,109,117],"derived":[20],"from":[21],"machine":[22],"learning":[23],"techniques":[24],"using":[25],"artificial":[26],"neural":[27],"networks":[28],"with":[29,66],"Gaussian":[30],"radial":[31],"basis":[32],"functions":[33],"their":[35],"neurons.":[36],"The":[37],"proposed":[38,71,110],"method":[39,111],"incrementally":[40],"develops":[41],"an":[42],"approximation":[43],"through":[44],"optimization":[46],"scalar":[49],"condensed":[50],"form":[51],"equations.":[55],"Unlike":[56],"traditional":[57,125],"solvers":[58],"that":[59,116,123],"require":[60],"grids,":[61],"volumes,":[62],"or":[63,95],"meshes,":[64],"along":[65],"corresponding":[67],"connectivity":[68],"data,":[69],"requires":[73],"only":[74],"list":[76],"independent":[78],"variable":[79],"values":[80],"to":[81],"approximate":[82],"solution.":[84],"Because":[85],"this,":[87],"there":[88],"no":[90],"need":[91],"derivation":[94],"inversion":[96],"system":[98],"matrices.":[99],"Results":[100],"are":[101],"demonstrating":[103],"stability":[105],"and":[106,112],"accuracy":[107],"it":[113],"demonstrated":[115],"spatial":[118],"error":[119],"estimate":[120],"can":[121],"exceed":[122],"methods.":[126]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}