{"id":"https://openalex.org/W4389055815","doi":"https://doi.org/10.3390/a16120537","title":"Comparing Activation Functions in Machine Learning for Finite Element Simulations in Thermomechanical Forming","display_name":"Comparing Activation Functions in Machine Learning for Finite Element Simulations in Thermomechanical Forming","publication_year":2023,"publication_date":"2023-11-25","ids":{"openalex":"https://openalex.org/W4389055815","doi":"https://doi.org/10.3390/a16120537"},"language":"en","primary_location":{"id":"doi:10.3390/a16120537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16120537","pdf_url":"https://www.mdpi.com/1999-4893/16/12/537/pdf?version=1701007271","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/12/537/pdf?version=1701007271","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011136435","display_name":"Olivier Pantal\u00e9","orcid":"https://orcid.org/0000-0001-7367-5453"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I4210130517","display_name":"Laboratoire G\u00e9nie de Production","ror":"https://ror.org/039aqbp11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I119865316","https://openalex.org/I4210130517","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I119865316","display_name":"\u00c9cole Nationale d'Ing\u00e9nieurs de Tarbes","ror":"https://ror.org/01fdvj254","country_code":"FR","type":"education","lineage":["https://openalex.org/I119865316","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Olivier Pantal\u00e9","raw_affiliation_strings":["Laboratoire G\u00e9nie de Production, Institut National Polytechnique/Ecole Nationale d\u2019Ing\u00e9nieurs de Tarbes, Universit\u00e9 de Toulouse, 47 Av d\u2019Azereix, F-65016 Tarbes, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire G\u00e9nie de Production, Institut National Polytechnique/Ecole Nationale d\u2019Ing\u00e9nieurs de Tarbes, Universit\u00e9 de Toulouse, 47 Av d\u2019Azereix, F-65016 Tarbes, France","institution_ids":["https://openalex.org/I119865316","https://openalex.org/I4210130517","https://openalex.org/I17866349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011136435"],"corresponding_institution_ids":["https://openalex.org/I119865316","https://openalex.org/I17866349","https://openalex.org/I4210130517"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.0486,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85276537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"16","issue":"12","first_page":"537","last_page":"537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11201","display_name":"Metallurgy and Material Forming","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11201","display_name":"Metallurgy and Material Forming","score":0.9995999932289124,"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/T10700","display_name":"Metal Forming Simulation Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10386","display_name":"Microstructure and Mechanical Properties of Steels","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/subroutine","display_name":"Subroutine","score":0.8891618251800537},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.7733265161514282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7001110911369324},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.6858696937561035},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6816419363021851},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6776123642921448},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5719478130340576},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5362033247947693},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5181580781936646},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.5012149810791016},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.4816359579563141},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46568503975868225},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41046249866485596},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4029281735420227},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3786904215812683},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.1717655062675476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.13550755381584167},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08699053525924683}],"concepts":[{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.8891618251800537},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.7733265161514282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7001110911369324},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6858696937561035},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6816419363021851},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6776123642921448},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5719478130340576},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5362033247947693},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5181580781936646},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.5012149810791016},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4816359579563141},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46568503975868225},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41046249866485596},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4029281735420227},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3786904215812683},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.1717655062675476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13550755381584167},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08699053525924683},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a16120537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16120537","pdf_url":"https://www.mdpi.com/1999-4893/16/12/537/pdf?version=1701007271","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04316232v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04316232","pdf_url":"https://hal.science/hal-04316232/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, 2023, 16 (12), pp.537. &#x27E8;10.3390/a16120537&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:a1505c97f6524c6298b424c3f685cf41","is_oa":true,"landing_page_url":"https://doaj.org/article/a1505c97f6524c6298b424c3f685cf41","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 16, Iss 12, p 537 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a16120537","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16120537","pdf_url":"https://www.mdpi.com/1999-4893/16/12/537/pdf?version=1701007271","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389055815.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1612808768","https://openalex.org/W1976245556","https://openalex.org/W2012544830","https://openalex.org/W2054490887","https://openalex.org/W2058418186","https://openalex.org/W2080123636","https://openalex.org/W2080296771","https://openalex.org/W2137983211","https://openalex.org/W2502631026","https://openalex.org/W2873839375","https://openalex.org/W2891462664","https://openalex.org/W2907685416","https://openalex.org/W2908963506","https://openalex.org/W2917421740","https://openalex.org/W2944192730","https://openalex.org/W3027561281","https://openalex.org/W3097724114","https://openalex.org/W3155890069","https://openalex.org/W3207363415","https://openalex.org/W4210885031","https://openalex.org/W4283791586","https://openalex.org/W4285719527","https://openalex.org/W4293729994","https://openalex.org/W4294713908","https://openalex.org/W4316465563","https://openalex.org/W4318200154","https://openalex.org/W4327519603","https://openalex.org/W4353065045","https://openalex.org/W6744805438"],"related_works":["https://openalex.org/W4211198594","https://openalex.org/W4295036712","https://openalex.org/W2811324119","https://openalex.org/W4385451479","https://openalex.org/W3216434047","https://openalex.org/W3110577345","https://openalex.org/W2889196975","https://openalex.org/W3175461337","https://openalex.org/W2016147052","https://openalex.org/W2906090557"],"abstract_inverted_index":{"Finite":[0],"element":[1],"(FE)":[2],"simulations":[3,134],"have":[4],"been":[5],"effective":[6],"in":[7,40,53,139],"simulating":[8],"thermomechanical":[9],"forming":[10],"processes,":[11],"yet":[12],"challenges":[13],"arise":[14],"when":[15],"applying":[16],"them":[17],"to":[18,22,50],"new":[19],"materials":[20],"due":[21],"nonlinear":[23],"behaviors.":[24],"To":[25],"address":[26],"this,":[27],"machine":[28],"learning":[29],"techniques":[30],"and":[31,67,90,100,116,132],"artificial":[32,58],"neural":[33,59],"networks":[34],"play":[35],"an":[36,47,57],"increasingly":[37],"vital":[38],"role":[39],"developing":[41],"complex":[42],"models.":[43],"This":[44],"paper":[45],"presents":[46],"innovative":[48],"approach":[49],"parameter":[51],"identification":[52],"flow":[54],"laws,":[55],"utilizing":[56],"network":[60],"that":[61],"learns":[62],"directly":[63],"from":[64,129],"test":[65],"data":[66,128],"automatically":[68],"generates":[69],"a":[70],"Fortran":[71],"subroutine":[72],"for":[73],"the":[74,83,101,110,136,140],"Abaqus":[75,141],"standard":[76],"or":[77],"explicit":[78,142],"FE":[79,143],"codes.":[80],"We":[81],"investigate":[82],"impact":[84],"of":[85],"activation":[86],"functions":[87],"on":[88],"prediction":[89],"computational":[91],"efficiency":[92],"by":[93],"comparing":[94,123],"Sigmoid,":[95],"Tanh,":[96],"ReLU,":[97],"Swish,":[98],"Softplus,":[99],"less":[102],"common":[103],"Exponential":[104,111],"function.":[105],"Despite":[106],"its":[107],"infrequent":[108],"use,":[109],"function":[112],"demonstrates":[113],"noteworthy":[114],"performance":[115],"reduced":[117],"computation":[118],"times.":[119],"Model":[120],"validation":[121],"involves":[122],"predictive":[124],"capabilities":[125],"with":[126],"experimental":[127],"compression":[130],"tests,":[131],"numerical":[133,137],"confirm":[135],"implementation":[138],"code.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}
