{"id":"https://openalex.org/W7128716137","doi":"https://doi.org/10.1149/1945-7111/aebeff","title":"Out-of-Sample Voltage Prediction for PEM Electrolyzers via Knowledge Distillation to a Physics-Based Model","display_name":"Out-of-Sample Voltage Prediction for PEM Electrolyzers via Knowledge Distillation to a Physics-Based Model","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7128716137","doi":"https://doi.org/10.1149/1945-7111/aebeff"},"language":"en","primary_location":{"id":"doi:10.1149/1945-7111/aebeff","doi":"https://doi.org/10.1149/1945-7111/aebeff","is_oa":true,"landing_page_url":"https://doi.org/10.1149/1945-7111/aebeff","pdf_url":"https://iopscience.iop.org/article/10.1149/1945-7111/aebeff/pdf","source":{"id":"https://openalex.org/S138759888","display_name":"Journal of The Electrochemical Society","issn_l":"0013-4651","issn":["0013-4651","1945-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of The Electrochemical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://iopscience.iop.org/article/10.1149/1945-7111/aebeff/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125771536","display_name":"Hasan Asy'ari Arief","orcid":"https://orcid.org/0000-0002-8236-7046","observed_orcids":["https://orcid.org/0000-0002-8236-7046"]},"institutions":[{"id":"https://openalex.org/I4210107808","display_name":"NORCE Research AS","ror":"https://ror.org/02gagpf75","country_code":"NO","type":"facility","lineage":["https://openalex.org/I4210107808"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Hasan Asy'ari Arief","raw_affiliation_strings":["NORCE Norwegian Research Centre AS"],"raw_orcid":"https://orcid.org/0000-0002-8236-7046","affiliations":[{"raw_affiliation_string":"NORCE Norwegian Research Centre AS","institution_ids":["https://openalex.org/I4210107808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043808831","display_name":"Kjersti Wergeland Krakhella","orcid":"https://orcid.org/0000-0002-5931-3269","observed_orcids":["https://orcid.org/0000-0002-5931-3269"]},"institutions":[{"id":"https://openalex.org/I4210107808","display_name":"NORCE Research AS","ror":"https://ror.org/02gagpf75","country_code":"NO","type":"facility","lineage":["https://openalex.org/I4210107808"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Kjersti Wergeland Wergeland Krakhella","raw_affiliation_strings":["NORCE Norwegian Research Centre AS"],"raw_orcid":"https://orcid.org/0000-0002-5931-3269","affiliations":[{"raw_affiliation_string":"NORCE Norwegian Research Centre AS","institution_ids":["https://openalex.org/I4210107808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028075451","display_name":"Jonas S\u00f8mod Ahmed","orcid":"https://orcid.org/0009-0005-1257-628X","observed_orcids":["https://orcid.org/0009-0005-1257-628X"]},"institutions":[{"id":"https://openalex.org/I4210107808","display_name":"NORCE Research AS","ror":"https://ror.org/02gagpf75","country_code":"NO","type":"facility","lineage":["https://openalex.org/I4210107808"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Jonas S\u00f8mod Ahmed","raw_affiliation_strings":["NORCE Norwegian Research Centre AS"],"raw_orcid":"https://orcid.org/0009-0005-1257-628X","affiliations":[{"raw_affiliation_string":"NORCE Norwegian Research Centre AS","institution_ids":["https://openalex.org/I4210107808"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008089558","display_name":"Dmitry Bokach","orcid":"https://orcid.org/0000-0002-1073-9883","observed_orcids":["https://orcid.org/0000-0002-1073-9883"]},"institutions":[{"id":"https://openalex.org/I4210107808","display_name":"NORCE Research AS","ror":"https://ror.org/02gagpf75","country_code":"NO","type":"facility","lineage":["https://openalex.org/I4210107808"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Dmitry Bokach","raw_affiliation_strings":["NORCE Norwegian Research Centre AS"],"raw_orcid":"https://orcid.org/0000-0002-1073-9883","affiliations":[{"raw_affiliation_string":"NORCE Norwegian Research Centre AS","institution_ids":["https://openalex.org/I4210107808"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210107808"],"apc_list":{"value":1950,"currency":"USD","value_usd":1950},"apc_paid":{"value":1950,"currency":"USD","value_usd":1950},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10409","display_name":"Fuel Cells and Related Materials","score":0.951200008392334,"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"}},"topics":[{"id":"https://openalex.org/T10409","display_name":"Fuel Cells and Related Materials","score":0.951200008392334,"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"}},{"id":"https://openalex.org/T10030","display_name":"Electrocatalysts for Energy Conversion","score":0.03310000151395798,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/proton-exchange-membrane-electrolyzer","display_name":"proton exchange membrane electrolyzer","score":0.9539999961853027},{"id":"https://openalex.org/keywords/out-of-sample-forecasting","display_name":"out-of-sample forecasting","score":0.9419999718666077},{"id":"https://openalex.org/keywords/knowledge-distillation","display_name":"knowledge distillation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/physics-based-modeling","display_name":"physics-based modeling","score":0.6919999718666077},{"id":"https://openalex.org/keywords/hybrid-physics-machine-learning-models","display_name":"hybrid physics-machine learning models","score":0.5410000085830688},{"id":"https://openalex.org/keywords/nernst-equation","display_name":"Nernst equation","score":0.8690000176429749},{"id":"https://openalex.org/keywords/butler-volmer-kinetics","display_name":"Butler-Volmer kinetics","score":0.9079999923706055},{"id":"https://openalex.org/keywords/closed-form-model","display_name":"closed-form model","score":0.5519999861717224}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7336999773979187},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6255000233650208},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6011999845504761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5026000142097473},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.4855000078678131},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4187000095844269},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.38449999690055847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3743000030517578},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35519999265670776},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2971999943256378},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.29409998655319214},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C55037315","wikidata":"https://www.wikidata.org/wiki/Q5421151","display_name":"Experimental data","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C72293138","wikidata":"https://www.wikidata.org/wiki/Q909741","display_name":"Temperature measurement","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1149/1945-7111/aebeff","doi":"https://doi.org/10.1149/1945-7111/aebeff","is_oa":true,"landing_page_url":"https://doi.org/10.1149/1945-7111/aebeff","pdf_url":"https://iopscience.iop.org/article/10.1149/1945-7111/aebeff/pdf","source":{"id":"https://openalex.org/S138759888","display_name":"Journal of The Electrochemical Society","issn_l":"0013-4651","issn":["0013-4651","1945-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of The Electrochemical Society","raw_type":"journal-article"},{"id":"doi:10.2139/ssrn.6225603","doi":"https://doi.org/10.2139/ssrn.6225603","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.6225603","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.1149/1945-7111/aebeff","doi":"https://doi.org/10.1149/1945-7111/aebeff","is_oa":true,"landing_page_url":"https://doi.org/10.1149/1945-7111/aebeff","pdf_url":"https://iopscience.iop.org/article/10.1149/1945-7111/aebeff/pdf","source":{"id":"https://openalex.org/S138759888","display_name":"Journal of The Electrochemical Society","issn_l":"0013-4651","issn":["0013-4651","1945-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310311669","host_organization_name":"Institute of Physics","host_organization_lineage":["https://openalex.org/P4310311669"],"host_organization_lineage_names":["Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of The Electrochemical Society","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.878000020980835,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128716137.pdf","grobid_xml":"https://content.openalex.org/works/W7128716137.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1821462560","https://openalex.org/W1981732190","https://openalex.org/W1984717573","https://openalex.org/W2019410740","https://openalex.org/W2020007931","https://openalex.org/W2036699254","https://openalex.org/W2774086071","https://openalex.org/W2803118351","https://openalex.org/W2890961624","https://openalex.org/W2899283552","https://openalex.org/W2905218447","https://openalex.org/W2924382816","https://openalex.org/W3011231583","https://openalex.org/W3034756453","https://openalex.org/W3163993681","https://openalex.org/W4214511508","https://openalex.org/W4280593344","https://openalex.org/W4398164319","https://openalex.org/W4399661307","https://openalex.org/W4401797956","https://openalex.org/W4404771489","https://openalex.org/W4406289245","https://openalex.org/W4409909448","https://openalex.org/W4414272882","https://openalex.org/W7165791928"],"related_works":["https://openalex.org/W7203713958","https://openalex.org/W7160912895","https://openalex.org/W7211188514","https://openalex.org/W4206170484","https://openalex.org/W4406958314","https://openalex.org/W3041723680","https://openalex.org/W4412733878","https://openalex.org/W3092300240","https://openalex.org/W4408342366","https://openalex.org/W3129048471"],"abstract_inverted_index":{"Abstract":[0],"Voltage":[1],"models":[2],"for":[3],"Proton":[4],"Exchange":[5],"Membrane":[6],"(PEM)":[7],"electrolyzers":[8],"calibrated":[9],"under":[10,22],"one":[11],"set":[12],"of":[13,94,104,140],"operating":[14,113],"conditions":[15],"often":[16],"fail":[17],"when":[18],"required":[19],"to":[20],"predict":[21],"different":[23,112],"conditions,":[24],"a":[25,44,58,66,74,99,137],"task":[26],"known":[27],"in":[28,42],"machine":[29],"learning":[30],"as":[31],"Out-of-Sample":[32],"(OOS)":[33],"prediction.":[34],"We":[35],"address":[36],"this":[37],"problem":[38],"with":[39,57,98,111],"knowledge":[40],"distillation,":[41],"which":[43],"hybrid":[45],"teacher":[46],"combining":[47],"the":[48,85,95],"electrochemical":[49,145],"equations":[50],"(Nernst":[51],"equation,":[52],"Butler\u2013Volmer":[53],"kinetics,":[54],"Ohm's":[55],"law)":[56],"bounded":[59],"neural":[60],"network":[61],"correction":[62,149],"is":[63,136],"distilled":[64],"into":[65],"12-parameter":[67],"physics-based":[68],"student.":[69],"Using":[70],"OOS":[71],"datasets":[72],"from":[73],"Static":[75],"Water":[76],"Vapour":[77],"Feed":[78],"(SWVF)":[79],"PEM":[80],"electrolyzer,":[81],"we":[82],"show":[83],"that":[84],"student":[86],"predicts":[87],"voltage":[88],"more":[89],"accurately":[90],"than":[91,118,128],"conventional":[92],"fitting":[93,130],"same":[96],"equations,":[97],"mean":[100],"absolute":[101],"error":[102],"(MAE)":[103],"9.2":[105],"mV":[106],"across":[107],"two":[108],"evaluation":[109],"campaigns":[110],"protocols,":[114],"approximately":[115],"75%":[116],"lower":[117,127],"Levenberg\u2013Marquardt":[119],"nonlinear":[120],"least":[121],"squares":[122],"(37.2":[123],"mV)":[124],"and":[125,151],"70%":[126],"gradient-based":[129],"(30.4":[131],"mV).":[132],"The":[133],"deployed":[134],"model":[135],"closed-form":[138],"expression":[139],"12":[141],"constants":[142],"(six":[143],"effective":[144],"parameters,":[146],"six":[147],"empirical":[148],"constants)":[150],"runs":[152],"without":[153],"machine-learning":[154],"software.":[155]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-02-13T00:00:00"}