{"id":"https://openalex.org/W4404847696","doi":"https://doi.org/10.1109/access.2024.3508735","title":"Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning","display_name":"Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4404847696","doi":"https://doi.org/10.1109/access.2024.3508735"},"language":"en","primary_location":{"id":"doi:10.1109/access.2024.3508735","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3508735","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2024.3508735","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043966041","display_name":"Farhad Pourkamali\u2010Anaraki","orcid":"https://orcid.org/0000-0003-4078-1676"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Farhad Pourkamali-Anaraki","raw_affiliation_strings":["Department of Mathematical and Statistical Sciences, University of Colorado at Denver, Denver, CO, USA","Department of Mathematical and Statistical Sciences, University of Colorado, Denver, CO, USA"],"raw_orcid":"https://orcid.org/0000-0003-4078-1676","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Statistical Sciences, University of Colorado at Denver, Denver, CO, USA","institution_ids":["https://openalex.org/I921990950"]},{"raw_affiliation_string":"Department of Mathematical and Statistical Sciences, University of Colorado, Denver, CO, USA","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040509852","display_name":"Jamal F. Husseini","orcid":null},"institutions":[{"id":"https://openalex.org/I133738476","display_name":"University of Massachusetts Lowell","ror":"https://ror.org/03hamhx47","country_code":"US","type":"education","lineage":["https://openalex.org/I133738476"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jamal F. Husseini","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USA","Department of Mechanical and Industrial Engineering, University of Massachusetts, Lowell, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USA","institution_ids":["https://openalex.org/I133738476"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, University of Massachusetts, Lowell, MA, USA","institution_ids":["https://openalex.org/I133738476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091024583","display_name":"Scott E. Stapleton","orcid":"https://orcid.org/0000-0003-4834-9992"},"institutions":[{"id":"https://openalex.org/I133738476","display_name":"University of Massachusetts Lowell","ror":"https://ror.org/03hamhx47","country_code":"US","type":"education","lineage":["https://openalex.org/I133738476"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott E. Stapleton","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USA","Department of Mechanical and Industrial Engineering, University of Massachusetts, Lowell, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USA","institution_ids":["https://openalex.org/I133738476"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, University of Massachusetts, Lowell, MA, USA","institution_ids":["https://openalex.org/I133738476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.113,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89437569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":null,"first_page":"178816","last_page":"178831"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.5095000267028809,"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/T10320","display_name":"Neural Networks and Applications","score":0.5095000267028809,"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/T14351","display_name":"Statistical and Computational Modeling","score":0.498199999332428,"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/T14470","display_name":"Advanced Data Processing Techniques","score":0.44609999656677246,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6748583316802979},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6499009132385254},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.6079927682876587},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6013667583465576},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.569577693939209}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6748583316802979},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6499009132385254},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.6079927682876587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6013667583465576},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.569577693939209}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2024.3508735","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3508735","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0bacf2bb71724e739fe8fb0c7c7a34d8","is_oa":true,"landing_page_url":"https://doaj.org/article/0bacf2bb71724e739fe8fb0c7c7a34d8","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 12, Pp 178816-178831 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2024.3508735","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2024.3508735","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7007111814","display_name":null,"funder_award_id":"80NSSC21K1285","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"},{"id":"https://openalex.org/G711293417","display_name":null,"funder_award_id":"80NSSC21N0102","funder_id":"https://openalex.org/F4320316895","funder_display_name":"Aeronautics Research Mission Directorate"}],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320316895","display_name":"Aeronautics Research Mission Directorate","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1667249920","https://openalex.org/W2088319833","https://openalex.org/W2100011707","https://openalex.org/W2171280873","https://openalex.org/W2494454509","https://openalex.org/W2496754111","https://openalex.org/W2565516711","https://openalex.org/W2742757407","https://openalex.org/W2793244874","https://openalex.org/W2804446681","https://openalex.org/W2948978827","https://openalex.org/W2959938226","https://openalex.org/W2997591727","https://openalex.org/W3009955490","https://openalex.org/W3014596384","https://openalex.org/W3041549894","https://openalex.org/W3046336220","https://openalex.org/W3046812802","https://openalex.org/W3048374358","https://openalex.org/W3094019383","https://openalex.org/W3122204424","https://openalex.org/W3125468312","https://openalex.org/W3126856044","https://openalex.org/W3158148831","https://openalex.org/W3183048323","https://openalex.org/W3189164715","https://openalex.org/W3195180572","https://openalex.org/W3199238138","https://openalex.org/W3204236384","https://openalex.org/W3209295695","https://openalex.org/W4205164650","https://openalex.org/W4213248101","https://openalex.org/W4221083529","https://openalex.org/W4285082580","https://openalex.org/W4285147827","https://openalex.org/W4286797646","https://openalex.org/W4306933196","https://openalex.org/W4308798344","https://openalex.org/W4313594290","https://openalex.org/W4315628777","https://openalex.org/W4317584045","https://openalex.org/W4319074048","https://openalex.org/W4323644307","https://openalex.org/W4324325927","https://openalex.org/W4327519603","https://openalex.org/W4378528083","https://openalex.org/W4382239711","https://openalex.org/W4386133003","https://openalex.org/W4386337006","https://openalex.org/W4386575673","https://openalex.org/W4387762676","https://openalex.org/W4387910965","https://openalex.org/W4388948923","https://openalex.org/W4389392955","https://openalex.org/W4389763759","https://openalex.org/W4391709566","https://openalex.org/W4392896772","https://openalex.org/W4392934848","https://openalex.org/W4393156899","https://openalex.org/W4403482212","https://openalex.org/W6718212895","https://openalex.org/W6740256410","https://openalex.org/W6810059299","https://openalex.org/W6810099309","https://openalex.org/W6839471541","https://openalex.org/W6847745331"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W4394896187","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W3107602296","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347"],"abstract_inverted_index":{"This":[0],"paper":[1,65],"investigates":[2],"the":[3,17,21,47,51,67,79,113,164,169],"use":[4],"of":[5,24,53,63,69,81,151,167,173],"probabilistic":[6,71],"neural":[7,36,174],"networks":[8,37,175],"(PNNs)":[9],"to":[10,16,74,108,163,176],"model":[11,104],"aleatoric":[12,105],"uncertainty,":[13,106],"which":[14],"refers":[15],"inherent":[18],"variability":[19],"in":[20,59,83,123,181],"input-output":[22,179],"relationships":[23,180],"a":[25,70,90,124,147],"system,":[26],"often":[27],"characterized":[28],"by":[29],"unequal":[30],"variance":[31],"or":[32],"heteroscedasticity.":[33],"Unlike":[34],"traditional":[35],"that":[38,101],"produce":[39],"deterministic":[40],"outputs,":[41],"PNNs":[42,82,102,130],"generate":[43],"probability":[44],"distributions":[45],"for":[46,119],"target":[48],"variable,":[49],"allowing":[50],"determination":[52],"both":[54],"predicted":[55,144],"means":[56],"and":[57,78,142],"variances":[58,145],"regression":[60,118],"scenarios.":[61],"Contributions":[62],"this":[64,120,160],"include":[66],"development":[68],"distance":[72],"metric":[73],"optimize":[75],"PNN":[76],"architecture,":[77],"deployment":[80],"controlled":[84],"data":[85,157],"sets":[86],"as":[87,89],"well":[88],"practical":[91],"material":[92],"science":[93],"case":[94],"involving":[95],"fiber-reinforced":[96],"composites.":[97],"The":[98],"findings":[99],"confirm":[100],"effectively":[103],"proving":[107],"be":[109],"more":[110],"appropriate":[111],"than":[112],"commonly":[114],"employed":[115],"Gaussian":[116],"process":[117],"purpose.":[121],"Specifically,":[122],"real-world":[125],"scientific":[126,182],"machine":[127],"learning":[128],"context,":[129],"yield":[131],"remarkably":[132],"accurate":[133],"output":[134],"mean":[135],"estimates":[136],"with":[137],"R-squared":[138],"scores":[139],"approaching":[140],"0.97,":[141],"their":[143],"exhibit":[146],"high":[148],"correlation":[149],"coefficient":[150],"nearly":[152],"0.77,":[153],"closely":[154],"matching":[155],"observed":[156],"variances.":[158],"Hence,":[159],"research":[161],"contributes":[162],"ongoing":[165],"exploration":[166],"leveraging":[168],"sophisticated":[170],"representational":[171],"capacity":[172],"delineate":[177],"complex":[178],"problems.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2025-10-10T00:00:00"}