{"id":"https://openalex.org/W2555376095","doi":"https://doi.org/10.1109/ijcnn.2016.7727833","title":"A substitution of the general partial differential equation with extended polynomial networks","display_name":"A substitution of the general partial differential equation with extended polynomial networks","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2555376095","doi":"https://doi.org/10.1109/ijcnn.2016.7727833","mag":"2555376095"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2016.7727833","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2016.7727833","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-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/A5022710304","display_name":"Ladislav Zjavka","orcid":"https://orcid.org/0000-0002-2881-4319"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Ladislav Zjavka","raw_affiliation_strings":["Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011543714","display_name":"V\u00e1clav Sn\u00e5\u0161el","orcid":"https://orcid.org/0000-0002-9600-8319"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Vaclav Snasel","raw_affiliation_strings":["Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058318377","display_name":"Varun Ojha","orcid":"https://orcid.org/0000-0002-9256-1192"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Varun Kumar Ojha","raw_affiliation_strings":["Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003799782","display_name":"Witold Pedrycz","orcid":"https://orcid.org/0000-0002-9335-9930"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Witold Pedrycz","raw_affiliation_strings":["University of Alberta, Edmonton, AB, CA"],"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, AB, CA","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5022710304"],"corresponding_institution_ids":["https://openalex.org/I142208455"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12677444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":null,"first_page":"4819","last_page":"4826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9941999912261963,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9733999967575073,"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/partial-derivative","display_name":"Partial derivative","score":0.7074010968208313},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6870099902153015},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5898515582084656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5762748718261719},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5577648282051086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5269328355789185},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5137439966201782},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.48274701833724976},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.482623428106308},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48069292306900024},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.463384747505188},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.4174097180366516},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32876068353652954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28922173380851746}],"concepts":[{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.7074010968208313},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6870099902153015},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5898515582084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5762748718261719},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5577648282051086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5269328355789185},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5137439966201782},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.48274701833724976},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.482623428106308},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48069292306900024},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.463384747505188},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.4174097180366516},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32876068353652954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28922173380851746},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ijcnn.2016.7727833","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2016.7727833","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},{"id":"pmh:oai:centaur.reading.ac.uk:93555","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1536362902","https://openalex.org/W1696703109","https://openalex.org/W1981300217","https://openalex.org/W1982525615","https://openalex.org/W1999666923","https://openalex.org/W2006610075","https://openalex.org/W2013137720","https://openalex.org/W2016253569","https://openalex.org/W2023475317","https://openalex.org/W2034219729","https://openalex.org/W2036259226","https://openalex.org/W2056137745","https://openalex.org/W2059639738","https://openalex.org/W2068280365","https://openalex.org/W2071529495","https://openalex.org/W2077174186","https://openalex.org/W2124611117","https://openalex.org/W2141703670","https://openalex.org/W2146168695","https://openalex.org/W2168441430","https://openalex.org/W2178957972","https://openalex.org/W2188548788","https://openalex.org/W2468632786","https://openalex.org/W4233306889","https://openalex.org/W4285719527","https://openalex.org/W6653662649","https://openalex.org/W6685641422","https://openalex.org/W6719656640","https://openalex.org/W6814925325"],"related_works":["https://openalex.org/W2735653195","https://openalex.org/W1767607552","https://openalex.org/W2372663877","https://openalex.org/W2139348706","https://openalex.org/W2908477459","https://openalex.org/W120789411","https://openalex.org/W2782711679","https://openalex.org/W2776138620","https://openalex.org/W2160238255","https://openalex.org/W3081774625"],"abstract_inverted_index":{"General":[0],"partial":[1,45,73],"differential":[2,32,46,90],"equations,":[3],"which":[4,99],"can":[5],"describe":[6,71],"any":[7],"complex":[8,120],"functions,":[9],"may":[10,143],"be":[11],"solved":[12],"by":[13],"an":[14,54,137],"adapted":[15],"method":[16,115],"of":[17,26,42,61,76,79,109,147],"the":[18,43,72,145,148],"similarity":[19],"analysis":[20],"that":[21],"models":[22,126],"polynomial":[23,33,85,95,149],"data":[24,86],"relations":[25],"discrete":[27],"observations.":[28],"The":[29,88,113,131],"proposed":[30,114],"new":[31],"networks":[34,150],"define":[35],"and":[36,102,121,151],"substitute":[37],"for":[38],"a":[39,164],"selective":[40,124],"form":[41,118],"general":[44,89],"equation":[47,91],"using":[48],"fraction":[49],"derivative":[50,63,74,105,123,153],"units":[51],"to":[52,82,117,155],"model":[53],"unknown":[55],"system":[56,165],"or":[57,160],"pattern.":[58],"Convergent":[59],"series":[60,125],"relative":[62],"substitution":[64],"terms,":[65],"produced":[66],"in":[67,107,140,163],"all":[68],"network":[69,96],"layers,":[70],"changes":[75],"some":[77],"combinations":[78],"input":[80],"variables":[81],"generalize":[83],"elementary":[84],"relations.":[87],"is":[92],"decomposed":[93],"into":[94],"backward":[97],"structure,":[98],"defines":[100],"simple":[101],"composite":[103],"sum":[104],"terms":[106,154],"respect":[108],"previous":[110],"layers":[111],"variables.":[112],"enables":[116],"more":[119],"varied":[122],"than":[127],"standard":[128],"soft-computing":[129],"techniques.":[130],"sigmoidal":[132],"function,":[133],"commonly":[134],"employed":[135],"as":[136],"activation":[138],"function":[139],"artificial":[141],"neurons,":[142],"improve":[144],"abilities":[146],"substituting":[152],"approximate":[156],"complicated":[157],"periodic":[158],"multi-variable":[159],"time-series":[161],"functions":[162],"model.":[166]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}