{"id":"https://openalex.org/W2767540877","doi":"https://doi.org/10.1137/17m1155867","title":"Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media","display_name":"Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2767540877","doi":"https://doi.org/10.1137/17m1155867","mag":"2767540877"},"language":"en","primary_location":{"id":"doi:10.1137/17m1155867","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1155867","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.02475","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048628614","display_name":"Constantin Grigo","orcid":"https://orcid.org/0000-0003-4755-8485"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Constantin Grigo","raw_affiliation_strings":["Department of Mechanical Engineering, Technical University of Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4755-8485","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Technical University of Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053827070","display_name":"Phaedon\u2010Stelios Koutsourelakis","orcid":"https://orcid.org/0000-0002-9345-759X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Phaedon-Stelios Koutsourelakis","raw_affiliation_strings":["Department of Mechanical Engineering, Technical University of Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9345-759X","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Technical University of Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048628614"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":2.8229,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.92797407,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"292","last_page":"323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9969000220298767,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6213829517364502},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6072515845298767},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5648592710494995},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5633416175842285},{"id":"https://openalex.org/keywords/uncertainty-reduction-theory","display_name":"Uncertainty reduction theory","score":0.5269932150840759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4754588007926941},{"id":"https://openalex.org/keywords/random-effects-model","display_name":"Random effects model","score":0.45126819610595703},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.4411589801311493},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.40676116943359375},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.39719173312187195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35248863697052},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23989149928092957},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.1542673110961914},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07325905561447144}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6213829517364502},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6072515845298767},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5648592710494995},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5633416175842285},{"id":"https://openalex.org/C94361409","wikidata":"https://www.wikidata.org/wiki/Q7882500","display_name":"Uncertainty reduction theory","level":2,"score":0.5269932150840759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4754588007926941},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.45126819610595703},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4411589801311493},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.40676116943359375},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.39719173312187195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35248863697052},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23989149928092957},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.1542673110961914},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07325905561447144},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C46312422","wikidata":"https://www.wikidata.org/wiki/Q11024","display_name":"Communication","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C95190672","wikidata":"https://www.wikidata.org/wiki/Q815382","display_name":"Meta-analysis","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1155867","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1155867","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.02475","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.02475","pdf_url":"https://arxiv.org/pdf/1711.02475","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.02475","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.02475","pdf_url":"https://arxiv.org/pdf/1711.02475","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4994645416","display_name":null,"funder_award_id":"Subrpoject 22","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":99,"referenced_works":["https://openalex.org/W106225695","https://openalex.org/W656368203","https://openalex.org/W781784501","https://openalex.org/W1511986666","https://openalex.org/W1522301498","https://openalex.org/W1523989055","https://openalex.org/W1561442812","https://openalex.org/W1567512734","https://openalex.org/W1570770495","https://openalex.org/W1591346633","https://openalex.org/W1686946872","https://openalex.org/W1934412359","https://openalex.org/W1959608418","https://openalex.org/W1964260410","https://openalex.org/W1966922361","https://openalex.org/W1977046327","https://openalex.org/W1982770560","https://openalex.org/W1985261292","https://openalex.org/W1985926778","https://openalex.org/W1998028876","https://openalex.org/W2001141328","https://openalex.org/W2015655664","https://openalex.org/W2017337590","https://openalex.org/W2017489029","https://openalex.org/W2027725084","https://openalex.org/W2034222383","https://openalex.org/W2041779820","https://openalex.org/W2042996313","https://openalex.org/W2046598747","https://openalex.org/W2049633694","https://openalex.org/W2051331055","https://openalex.org/W2053186076","https://openalex.org/W2055689370","https://openalex.org/W2060682310","https://openalex.org/W2063978378","https://openalex.org/W2068370589","https://openalex.org/W2069999296","https://openalex.org/W2072128103","https://openalex.org/W2074176021","https://openalex.org/W2087292325","https://openalex.org/W2089062907","https://openalex.org/W2096969866","https://openalex.org/W2104156750","https://openalex.org/W2107710506","https://openalex.org/W2115606304","https://openalex.org/W2116251284","https://openalex.org/W2125027820","https://openalex.org/W2131049189","https://openalex.org/W2133041109","https://openalex.org/W2134560790","https://openalex.org/W2135046866","https://openalex.org/W2135561481","https://openalex.org/W2137512539","https://openalex.org/W2140595615","https://openalex.org/W2143591652","https://openalex.org/W2146571341","https://openalex.org/W2148154358","https://openalex.org/W2149775970","https://openalex.org/W2156007048","https://openalex.org/W2158240273","https://openalex.org/W2160842254","https://openalex.org/W2161024376","https://openalex.org/W2165363188","https://openalex.org/W2167061265","https://openalex.org/W2168970443","https://openalex.org/W2225156818","https://openalex.org/W2295099209","https://openalex.org/W2321957512","https://openalex.org/W2322316866","https://openalex.org/W2342442580","https://openalex.org/W2399388063","https://openalex.org/W2399435825","https://openalex.org/W2480685991","https://openalex.org/W2504619654","https://openalex.org/W2510161586","https://openalex.org/W2547853451","https://openalex.org/W2557283755","https://openalex.org/W2567948266","https://openalex.org/W2592158694","https://openalex.org/W2594639291","https://openalex.org/W2745110207","https://openalex.org/W2745141280","https://openalex.org/W2747778728","https://openalex.org/W2772709428","https://openalex.org/W2784733489","https://openalex.org/W2919115771","https://openalex.org/W2951493172","https://openalex.org/W2962821901","https://openalex.org/W3001675847","https://openalex.org/W3101380508","https://openalex.org/W3121471846","https://openalex.org/W3140968660","https://openalex.org/W3155932456","https://openalex.org/W4231109964","https://openalex.org/W4232285367","https://openalex.org/W4235057631","https://openalex.org/W4285719527","https://openalex.org/W4294562888","https://openalex.org/W4388319965"],"related_works":["https://openalex.org/W2407375987","https://openalex.org/W3049691116","https://openalex.org/W2505726097","https://openalex.org/W2010643158","https://openalex.org/W2106867672","https://openalex.org/W4310268968","https://openalex.org/W2950975704","https://openalex.org/W4297815943","https://openalex.org/W2053745677","https://openalex.org/W2189378472"],"abstract_inverted_index":{"Well-established":[0],"methods":[1],"for":[2],"the":[3,56,63,91,113,125,155,160,174,186,214,233],"solution":[4,114],"of":[5,31,43,55,62,77,86,98,112,115,124,153,188,202,204,210,219,232,239,241],"stochastic":[6],"partial":[7],"differential":[8],"equations":[9],"(SPDEs)":[10],"typically":[11],"struggle":[12],"in":[13,23,119,135,167,185],"problems":[14],"with":[15,132,200],"high-dimensional":[16,92],"inputs/outputs.":[17],"Such":[18],"difficulties":[19],"are":[20,35,59,130,141],"only":[21],"amplified":[22],"large-scale":[24],"applications":[25],"where":[26,191],"even":[27],"a":[28,71,87,95,106,116,136,207],"few":[29,208],"tens":[30,201,209],"full-order":[32,126,211],"model":[33,118,139,150,212,216],"runs":[34],"impracticable.":[36],"While":[37],"dimensionality":[38],"reduction":[39,170],"can":[40,194],"alleviate":[41],"some":[42],"these":[44],"issues,":[45],"it":[46],"is":[47,75,151,217],"not":[48],"known":[49],"which":[50,236],"and":[51,81,105,140,224],"how":[52],"many":[53],"features":[54,223],"(high-dimensional)":[57,64],"input":[58,93],"actually":[60],"predictive":[61,156],"output.":[65],"In":[66],"this":[67],"paper,":[68],"we":[69],"advocate":[70],"Bayesian":[72],"formulation":[73],"that":[74,89,109,123,163],"capable":[76,152,218],"performing":[78],"simultaneous":[79],"dimension":[80],"model-order":[82],"reduction.":[83],"It":[84],"consists":[85,238],"component":[88,108],"encodes":[90],"into":[94],"low-dimensional":[96],"set":[97],"feature":[99],"functions":[100],"by":[101],"employing":[102],"sparsity-inducing":[103],"priors":[104],"decoding":[107],"makes":[110],"use":[111],"coarse-grained":[117],"order":[120],"to":[121,159,197],"reconstruct":[122],"model.":[127],"Both":[128],"components":[129],"represented":[131],"latent":[133],"variables":[134],"probabilistic":[137],"graphical":[138],"simultaneously":[142],"trained":[143],"using":[144],"Stochastic":[145],"Variational":[146],"Inference":[147],"methods.":[148],"The":[149],"quantifying":[154],"uncertainty":[157,175],"due":[158],"information":[161],"loss":[162],"unavoidably":[164],"takes":[165],"place":[166],"any":[168],"model-order/dimension":[169],"as":[171,173],"well":[172],"arising":[176],"from":[177],"finite-sized":[178],"training":[179],"datasets.":[180],"We":[181],"demonstrate":[182],"its":[183],"capabilities":[184],"context":[187],"random":[189,198],"media":[190],"fine-scale":[192],"fluctuations":[193],"give":[195],"rise":[196],"inputs":[199],"thousands":[203,240],"variables.":[205],"With":[206],"simulations,":[213],"proposed":[215],"identifying":[220],"salient":[221],"physical":[222],"producing":[225],"sharp":[226],"predictions":[227],"under":[228],"different":[229],"boundary":[230],"conditions":[231],"full":[234],"output":[235],"itself":[237],"components.":[242]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}