{"id":"https://openalex.org/W4310856212","doi":"https://doi.org/10.1016/j.jcp.2022.111810","title":"Multi-scale physics-informed machine learning using the Buckingham Pi theorem","display_name":"Multi-scale physics-informed machine learning using the Buckingham Pi theorem","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4310856212","doi":"https://doi.org/10.1016/j.jcp.2022.111810"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2022.111810","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5000863960","display_name":"Michael W. Oppenheimer","orcid":null},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]},{"id":"https://openalex.org/I2799950915","display_name":"Wright-Patterson Air Force Base","ror":"https://ror.org/0097e1k27","country_code":"US","type":"other","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2799950915","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael W. Oppenheimer","raw_affiliation_strings":["Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America","institution_ids":["https://openalex.org/I1280414376","https://openalex.org/I2799950915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033565143","display_name":"David Doman","orcid":null},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]},{"id":"https://openalex.org/I2799950915","display_name":"Wright-Patterson Air Force Base","ror":"https://ror.org/0097e1k27","country_code":"US","type":"other","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2799950915","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David B. Doman","raw_affiliation_strings":["Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America","institution_ids":["https://openalex.org/I1280414376","https://openalex.org/I2799950915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012694291","display_name":"Justin D. Merrick","orcid":"https://orcid.org/0000-0001-9749-7022"},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]},{"id":"https://openalex.org/I2799950915","display_name":"Wright-Patterson Air Force Base","ror":"https://ror.org/0097e1k27","country_code":"US","type":"other","lineage":["https://openalex.org/I1330347796","https://openalex.org/I2799950915","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Justin D. Merrick","raw_affiliation_strings":["Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Autonomous Control Branch, 2210 Eighth Street, Bldg. 146, Rm. 305, WPAFB, OH 45433-7531, United States of America","institution_ids":["https://openalex.org/I1280414376","https://openalex.org/I2799950915"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000863960"],"corresponding_institution_ids":["https://openalex.org/I1280414376","https://openalex.org/I2799950915"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750,"provenance":"doaj"},"apc_paid":null,"fwci":1.832,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.999832,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":91},"biblio":{"volume":"474","issue":null,"first_page":"111810","last_page":"111810"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Physics-Informed Neural Networks for Scientific Computing","score":0.9992,"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":"Physics-Informed Neural Networks for Scientific Computing","score":0.9992,"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/T11582","display_name":"Nanofluidics and Nanopore Technology","score":0.9907,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10320","display_name":"Neural Network Fundamentals and Applications","score":0.9848,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimensionless-quantity","display_name":"Dimensionless quantity","score":0.6573288},{"id":"https://openalex.org/keywords/backpropagation-learning","display_name":"Backpropagation Learning","score":0.538031},{"id":"https://openalex.org/keywords/nonlinear-systems","display_name":"Nonlinear Systems","score":0.537096},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep Learning","score":0.522775},{"id":"https://openalex.org/keywords/radial-basis-function-networks","display_name":"Radial Basis Function Networks","score":0.521852},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function Approximation","score":0.518442},{"id":"https://openalex.org/keywords/similitude","display_name":"Similitude","score":0.49004543},{"id":"https://openalex.org/keywords/variables","display_name":"Variables","score":0.4409429},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.44005916}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.68454087},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.6573288},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4987564},{"id":"https://openalex.org/C143271835","wikidata":"https://www.wikidata.org/wiki/Q254515","display_name":"Similitude","level":2,"score":0.49004543},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4783337},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.47114578},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4525411},{"id":"https://openalex.org/C27574286","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Variables","level":2,"score":0.4409429},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4403313},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.44005916},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.43053848},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40429223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.356927},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.35148084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14362875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.110834986},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jcp.2022.111810","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":10,"referenced_works":["https://openalex.org/W2039710112","https://openalex.org/W2144460675","https://openalex.org/W2169633538","https://openalex.org/W2324861744","https://openalex.org/W2329854473","https://openalex.org/W2947971823","https://openalex.org/W2963454111","https://openalex.org/W3163993681","https://openalex.org/W4205616158","https://openalex.org/W4297779039"],"related_works":["https://openalex.org/W4382559908","https://openalex.org/W4376875328","https://openalex.org/W4375841781","https://openalex.org/W4311072340","https://openalex.org/W3035214572","https://openalex.org/W3033216323","https://openalex.org/W2393220471","https://openalex.org/W2342977227","https://openalex.org/W2323025356","https://openalex.org/W1560970988"],"abstract_inverted_index":{"Neural":[0],"networks":[1],"are":[2,22,84,228],"a":[3,92,152,160,180],"form":[4],"of":[5,35,52,58,61,73,95,148,199,240,243],"machine":[6],"learning":[7],"that":[8,30,55,98,230,232],"can":[9,88,109,135,236],"be":[10,89,110,136,165,188],"trained":[11,166,183],"to":[12,120,144,158,164,167,190,206,215],"estimate":[13],"relationships":[14,27,78],"between":[15,28,79,102,127,172,222],"variables":[16,29,83,87,149,196],"in":[17],"complex":[18],"physical":[19,53,74,100],"processes.":[20],"They":[21],"particularly":[23],"adept":[24],"at":[25,130,248],"estimating":[26],"lie":[31,56,197],"within":[32],"the":[33,59,62,67,71,76,116,146,193,200,233,241],"ranges":[34],"values":[36],"for":[37,124,138],"which":[38],"they":[39],"have":[40],"been":[41,225],"trained.":[42],"Their":[43],"performance":[44],"often":[45],"diminishes":[46],"when":[47,219],"tasked":[48],"with":[49],"generating":[50],"estimates":[51],"processes":[54],"outside":[57,198],"region":[60],"input":[63,80,104,174,195],"space":[64],"covered":[65],"by":[66,91,151],"training":[68,201],"set.":[69,202],"In":[70],"case":[72],"systems,":[75],"possible":[77],"and":[81,105,115,175],"output":[82,106,176],"limited.":[85],"Dimensional":[86],"replaced":[90],"smaller":[93],"number":[94,147],"dimensionless":[96,161,173,204],"parameters":[97,177],"enforce":[99,121],"limitations":[101],"dimensional":[103,113,185,194,217],"variables.":[107],"This":[108,133],"accomplished":[111],"using":[112,184,216],"analysis":[114],"Buckingham":[117],"Pi":[118],"theorem":[119],"or":[122],"test":[123],"dynamic":[125,220],"similitude":[126,221],"systems":[128,223,246],"operating":[129,247],"different":[131,249],"scales.":[132,250],"process":[134,235],"exploited":[137],"two":[139],"purposes.":[140],"The":[141,155],"first":[142],"is":[143,157],"reduce":[145],"correlated":[150],"neural":[153,162,181],"network.":[154],"second":[156],"allow":[159],"network":[163,182],"function":[168],"as":[169,213],"an":[170,208],"interpolator":[171],"even":[178],"though":[179],"data":[186,205],"would":[187],"required":[189],"extrapolate":[191],"if":[192],"Using":[203],"fit":[207],"input-output":[209],"relationship":[210],"generalizes":[211],"better,":[212],"compared":[214],"data,":[218],"has":[224],"achieved.":[226],"Examples":[227],"presented":[229],"demonstrate":[231],"proposed":[234],"enable":[237],"accurate":[238],"modeling":[239],"behavior":[242],"physically":[244],"similar":[245]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4310856212","counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3}],"updated_date":"2024-09-30T19:43:50.553453","created_date":"2022-12-19"}
