{"id":"https://openalex.org/W4281669620","doi":"https://doi.org/10.1137/21m1432739","title":"Gaussian Process Subspace Prediction for Model Reduction","display_name":"Gaussian Process Subspace Prediction for Model Reduction","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4281669620","doi":"https://doi.org/10.1137/21m1432739"},"language":"en","primary_location":{"id":"doi:10.1137/21m1432739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432739","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"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/A5090054434","display_name":"Ruda Zhang","orcid":"https://orcid.org/0000-0002-2899-1008"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ruda Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102021624","display_name":"Simon Mak","orcid":"https://orcid.org/0000-0001-7872-1981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon Mak","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108072328","display_name":"David B. Dunson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Dunson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090054434"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5023,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81974849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"44","issue":"3","first_page":"A1428","last_page":"A1449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"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":"Model Reduction and Neural Networks","score":0.9998999834060669,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9970999956130981,"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/subspace-topology","display_name":"Subspace topology","score":0.7669227123260498},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6762900948524475},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5596978664398193},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5572863221168518},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5383201241493225},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5128300786018372},{"id":"https://openalex.org/keywords/random-subspace-method","display_name":"Random subspace method","score":0.47157683968544006},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.46622610092163086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43307697772979736},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41987118124961853},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.41604551672935486},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23764419555664062},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19923362135887146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10078546404838562}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7669227123260498},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6762900948524475},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5596978664398193},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5572863221168518},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5383201241493225},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5128300786018372},{"id":"https://openalex.org/C106135958","wikidata":"https://www.wikidata.org/wiki/Q7291993","display_name":"Random subspace method","level":3,"score":0.47157683968544006},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.46622610092163086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43307697772979736},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41987118124961853},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.41604551672935486},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23764419555664062},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19923362135887146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10078546404838562},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1432739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432739","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5923901538","display_name":null,"funder_award_id":"N00014-21-1-2510-01","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5963970009","display_name":null,"funder_award_id":"DMS-1638521","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W8105021","https://openalex.org/W1856452060","https://openalex.org/W1966992674","https://openalex.org/W1976406204","https://openalex.org/W2001669569","https://openalex.org/W2014356541","https://openalex.org/W2045512849","https://openalex.org/W2049753327","https://openalex.org/W2061320421","https://openalex.org/W2064733273","https://openalex.org/W2074889471","https://openalex.org/W2079630523","https://openalex.org/W2080556931","https://openalex.org/W2098720801","https://openalex.org/W2117756735","https://openalex.org/W2120516507","https://openalex.org/W2125275885","https://openalex.org/W2152896489","https://openalex.org/W2217724233","https://openalex.org/W2312884521","https://openalex.org/W2618462867","https://openalex.org/W2962875621","https://openalex.org/W2963346868","https://openalex.org/W2963448920","https://openalex.org/W2963832692","https://openalex.org/W2964008022","https://openalex.org/W2977689784","https://openalex.org/W2989768142","https://openalex.org/W3006275387","https://openalex.org/W3044566039","https://openalex.org/W3084318518","https://openalex.org/W3098133464","https://openalex.org/W3159369427","https://openalex.org/W3190675727","https://openalex.org/W4211049957","https://openalex.org/W4234552385","https://openalex.org/W4235606958","https://openalex.org/W4237236652","https://openalex.org/W4252750892","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W2896134808","https://openalex.org/W3172436493","https://openalex.org/W4287164812","https://openalex.org/W2007593166","https://openalex.org/W2957492749","https://openalex.org/W1887135636","https://openalex.org/W2094490861","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W1603777065"],"abstract_inverted_index":{"Subspace-valued":[0],"functions":[1,46],"arise":[2],"in":[3],"a":[4,29,62,96,112,119,147,151,164],"wide":[5],"range":[6],"of":[7,37,106,159],"problems,":[8],"including":[9],"parametric":[10],"reduced":[11,161,201],"order":[12],"modeling":[13],"(PROM),":[14],"parameter":[15,23,140,153],"reduction,":[16],"and":[17,55,80,118,174,216],"subspace":[18,68,73,136,191,214],"tracking.":[19],"In":[20],"PROM,":[21,143],"each":[22],"point":[24,154],"can":[25,52],"be":[26,53],"associated":[27],"with":[28,86,220],"subspace,":[30],"which":[31,51,132],"is":[32,78,176,205],"used":[33],"for":[34,67,122,134,178],"Petrov--Galerkin":[35],"projections":[36],"large":[38],"system":[39,172],"matrices.":[40],"Previous":[41],"efforts":[42],"to":[43,186,190],"approximate":[44],"such":[45],"use":[47],"interpolations":[48],"on":[49,90,100,171],"manifolds,":[50],"inaccurate":[54],"slow.":[56],"To":[57],"tackle":[58],"this,":[59],"we":[60],"propose":[61],"novel":[63],"Bayesian":[64],"nonparametric":[65],"model":[66,99,123],"prediction:":[69],"the":[70,83,91,101,104,139,144,157,206],"Gaussian":[71,88],"process":[72],"(GPS)":[74],"model.":[75],"This":[76],"method":[77,189],"extrinsic":[79],"intrinsic":[81],"at":[82,150,163],"same":[84],"time:":[85],"multivariate":[87],"distributions":[89],"Euclidean":[92],"space,":[93],"it":[94],"induces":[95],"joint":[97],"probability":[98],"Grassmann":[102],"manifold,":[103],"set":[105],"fixed-dimensional":[107],"subspaces.":[108],"The":[109],"GPS":[110,145,204],"adopts":[111],"simple":[113],"yet":[114],"general":[115],"correlation":[116],"structure,":[117],"principled":[120],"approach":[121],"selection.":[124],"Its":[125],"predictive":[126],"distribution":[127],"admits":[128],"an":[129],"analytical":[130],"form,":[131],"allows":[133],"efficient":[135,212],"prediction":[137,149],"over":[138],"space.":[141],"For":[142],"provides":[146],"probabilistic":[148],"new":[152],"that":[155,167,198],"retains":[156],"accuracy":[158],"local":[160,200],"models,":[162],"computational":[165],"complexity":[166],"does":[168],"not":[169],"depend":[170],"dimension,":[173],"thus":[175],"suitable":[177],"online":[179],"computation.":[180],"We":[181],"give":[182],"four":[183],"numerical":[184],"examples":[185],"compare":[187],"our":[188],"interpolation,":[192,215],"as":[193,195],"well":[194],"two":[196],"methods":[197],"interpolate":[199],"models.":[202],"Overall,":[203],"most":[207],"data":[208],"efficient,":[209],"more":[210],"computationally":[211],"than":[213],"gives":[217],"smooth":[218],"predictions":[219],"uncertainty":[221],"quantification.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}