{"id":"https://openalex.org/W4405938721","doi":"https://doi.org/10.3390/sym17010035","title":"Influence of the Neural Network Morphology Symmetry on the Complex Dynamic Objects\u2019 Diagnostics","display_name":"Influence of the Neural Network Morphology Symmetry on the Complex Dynamic Objects\u2019 Diagnostics","publication_year":2024,"publication_date":"2024-12-27","ids":{"openalex":"https://openalex.org/W4405938721","doi":"https://doi.org/10.3390/sym17010035"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010035","pdf_url":"https://www.mdpi.com/2073-8994/17/1/35/pdf?version=1735552970","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/1/35/pdf?version=1735552970","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083273780","display_name":"Serhii Vladov","orcid":"https://orcid.org/0000-0001-8009-5254"},"institutions":[{"id":"https://openalex.org/I4210120219","display_name":"Kharkiv National University of Internal Affairs","ror":"https://ror.org/02pkshz09","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210120219"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Serhii Vladov","raw_affiliation_strings":["Kremenchuk Flight College, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0001-8009-5254","affiliations":[{"raw_affiliation_string":"Kremenchuk Flight College, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine","institution_ids":["https://openalex.org/I4210120219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014873401","display_name":"Victoria Vysotska","orcid":"https://orcid.org/0000-0001-6417-3689"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Victoria Vysotska","raw_affiliation_strings":["Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0001-6417-3689","affiliations":[{"raw_affiliation_string":"Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062692549","display_name":"Viktor Vasylenko","orcid":"https://orcid.org/0000-0002-9313-861X"},"institutions":[{"id":"https://openalex.org/I4210120219","display_name":"Kharkiv National University of Internal Affairs","ror":"https://ror.org/02pkshz09","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210120219"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Viktor Vasylenko","raw_affiliation_strings":["Kremenchuk Flight College, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kremenchuk Flight College, Kharkiv National University of Internal Affairs, 27, L. Landau Avenue, 61080 Kharkiv, Ukraine","institution_ids":["https://openalex.org/I4210120219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030571810","display_name":"Vasyl Lytvyn","orcid":"https://orcid.org/0000-0002-9676-0180"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Vasyl Lytvyn","raw_affiliation_strings":["Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-9676-0180","affiliations":[{"raw_affiliation_string":"Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010975999","display_name":"Mariya Nazarkevych","orcid":"https://orcid.org/0000-0002-6528-9867"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Mariia Nazarkevych","raw_affiliation_strings":["Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-6528-9867","affiliations":[{"raw_affiliation_string":"Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028376355","display_name":"Olga Fedevych","orcid":"https://orcid.org/0000-0002-8170-3001"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Olha Fedevych","raw_affiliation_strings":["Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-8170-3001","affiliations":[{"raw_affiliation_string":"Information Systems and Networks Department, Lviv Polytechnic National University, 12, Bandera Street, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5028376355","https://openalex.org/A5083273780"],"corresponding_institution_ids":["https://openalex.org/I4210120219","https://openalex.org/I98435010"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36075659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","first_page":"35","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14512","display_name":"Technology and Human Factors in Education and Health","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T14512","display_name":"Technology and Human Factors in Education and Health","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T14470","display_name":"Advanced Data Processing Techniques","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T14438","display_name":"Advanced Scientific Research Methods","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7298535108566284},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6491786241531372},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5777133703231812},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5334228277206421},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5298440456390381},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5164914131164551},{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.4831390082836151},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.4524579644203186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43897777795791626},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43677079677581787},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42694610357284546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42527422308921814},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18723222613334656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16992133855819702},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.089763343334198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.088295578956604}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7298535108566284},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6491786241531372},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5777133703231812},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5334228277206421},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5298440456390381},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5164914131164551},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.4831390082836151},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.4524579644203186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43897777795791626},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43677079677581787},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42694610357284546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42527422308921814},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18723222613334656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16992133855819702},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.089763343334198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.088295578956604},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010035","pdf_url":"https://www.mdpi.com/2073-8994/17/1/35/pdf?version=1735552970","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9319103a58254a0683f9146692177443","is_oa":false,"landing_page_url":"https://doaj.org/article/9319103a58254a0683f9146692177443","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 35 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010035","pdf_url":"https://www.mdpi.com/2073-8994/17/1/35/pdf?version=1735552970","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321038","display_name":"Fonds National de la Recherche Luxembourg","ror":"https://ror.org/039z13y21"},{"id":"https://openalex.org/F4320324615","display_name":"Ministry of Education and Science of Ukraine","ror":"https://ror.org/03bra4w96"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405938721.pdf","grobid_xml":"https://content.openalex.org/works/W4405938721.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W2016288817","https://openalex.org/W2029394756","https://openalex.org/W2280154071","https://openalex.org/W2610345163","https://openalex.org/W2767762258","https://openalex.org/W2963802343","https://openalex.org/W2965279030","https://openalex.org/W2974671396","https://openalex.org/W3016328513","https://openalex.org/W3016747886","https://openalex.org/W3129086984","https://openalex.org/W3135061098","https://openalex.org/W3205438421","https://openalex.org/W3216640154","https://openalex.org/W4200584071","https://openalex.org/W4224439058","https://openalex.org/W4225983475","https://openalex.org/W4283753191","https://openalex.org/W4284879605","https://openalex.org/W4289768936","https://openalex.org/W4297541647","https://openalex.org/W4308083078","https://openalex.org/W4310287158","https://openalex.org/W4311255815","https://openalex.org/W4312280276","https://openalex.org/W4313427997","https://openalex.org/W4316659863","https://openalex.org/W4362705272","https://openalex.org/W4385758933","https://openalex.org/W4386435080","https://openalex.org/W4387101315","https://openalex.org/W4387941647","https://openalex.org/W4388183214","https://openalex.org/W4391529894","https://openalex.org/W4391667318","https://openalex.org/W4392043199","https://openalex.org/W4394010950","https://openalex.org/W4394982332","https://openalex.org/W4395682301","https://openalex.org/W4399456871","https://openalex.org/W4399665963","https://openalex.org/W4399858445","https://openalex.org/W4400198356","https://openalex.org/W4400447055","https://openalex.org/W4401483236","https://openalex.org/W4401577672","https://openalex.org/W4402371664","https://openalex.org/W4402708087","https://openalex.org/W4403079284","https://openalex.org/W4403684117","https://openalex.org/W4403944381","https://openalex.org/W4403978168","https://openalex.org/W4404091759","https://openalex.org/W4404319753","https://openalex.org/W4404387760","https://openalex.org/W6767924019","https://openalex.org/W6804436649","https://openalex.org/W6857426847","https://openalex.org/W6860760607"],"related_works":["https://openalex.org/W1980563100","https://openalex.org/W1644661642","https://openalex.org/W4297670902","https://openalex.org/W2035154026","https://openalex.org/W1975469967","https://openalex.org/W1973236628","https://openalex.org/W2346565650","https://openalex.org/W2067853971","https://openalex.org/W2084965710","https://openalex.org/W2114237124"],"abstract_inverted_index":{"In":[0,163],"this":[1,164],"article,":[2],"to":[3,39,54,64,137,154,171,226],"study":[4],"the":[5,31,41,51,55,65,72,79,89,95,106,116,120,131,145,174,187,199,210,216,231],"influence":[6],"of":[7],"neural":[8,42,66,97,108],"networks\u2019":[9,67],"morphology":[10],"symmetry,":[11],"a":[12,47,158,207],"mathematical":[13,28],"model":[14,29],"is":[15,44,62,82,101,113,141,178],"developed":[16,27],"that":[17,49,143,169,183,198,222],"considers":[18],"dynamic":[19,24,59],"symmetry":[20,60,212],"for":[21],"diagnosing":[22],"complex":[23],"objects.":[25],"The":[26,92,180,219],"includes":[30,126],"symmetric":[32,77,90,96,107,127,151,184,223],"architecture":[33],"concept":[34],"with":[35,84,150,173],"adaptive":[36],"parameters,":[37],"according":[38],"which":[40,112,125,129],"network":[43,98,109],"represented":[45],"by":[46,115],"function":[48,61,81,168],"relates":[50],"input":[52],"data":[53],"diagnostic":[56,217,232],"outputs.":[57],"A":[58],"introduced":[63],"weight":[68,161],"change":[69],"depending":[70],"on":[71],"systems\u2019":[73],"state.":[74,91],"To":[75],"achieve":[76],"training,":[78],"loss":[80,121],"minimised":[83],"regularisation":[85,152,185,201,224],"considering":[86],"deviations":[87],"from":[88],"theorem":[93],"\u201cOn":[94],"optimisation":[99,110],"stability\u201d":[100],"formulated":[102],"and":[103,119,133,157,190,213,229],"proven,":[104],"demonstrating":[105],"stability,":[111],"confirmed":[114],"weights\u2019":[117,176,188],"stability":[118],"functions\u2019":[122],"global":[123],"optimisation,":[124],"regularisation,":[128],"stabilises":[130],"weights":[132],"reduces":[134],"their":[135,192],"sensitivity":[136],"minor":[138],"disturbances.":[139],"It":[140,194],"shown":[142],"in":[144,160],"training":[146,228],"process,":[147],"gradient":[148],"descent":[149],"contributes":[153,225],"stable":[155],"convergence":[156],"decrease":[159],"asymmetry.":[162],"case,":[165],"an":[166],"energy":[167],"tends":[170],"zero":[172],"optimal":[175,200],"achievement":[177],"introduced.":[179],"analysis":[181],"showed":[182],"minimises":[186],"deviation":[189],"prevents":[191],"overtraining.":[193],"was":[195],"experimentally":[196],"established":[197],"coefficient":[202],"\u03bb":[203],"=":[204],"1.0":[205],"ensures":[206],"balance":[208],"between":[209],"models\u2019":[211,233],"flexibility,":[214],"minimising":[215],"error.":[218],"results":[220],"show":[221],"practical":[227],"increases":[230],"accuracy.":[234]},"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-01-01T00:00:00"}