{"id":"https://openalex.org/W3152645313","doi":"https://doi.org/10.1137/20m1354714","title":"Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior","display_name":"Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3152645313","doi":"https://doi.org/10.1137/20m1354714","mag":"3152645313"},"language":"en","primary_location":{"id":"doi:10.1137/20m1354714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1354714","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":["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/A5046387242","display_name":"Vi\u00eat H\u00e0 H\u00f2ang","orcid":"https://orcid.org/0000-0001-9990-5106"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Viet Ha Hoang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066037298","display_name":"Jia Hao Quek","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia Hao Quek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110448103","display_name":"Christoph Schwab","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Schwab","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0717,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78170898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"2","first_page":"384","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9896000027656555,"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/T10136","display_name":"Statistical Methods and Inference","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.8394513130187988},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6087909936904907},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5318925380706787},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5281493663787842},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5197089314460754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5127471685409546},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5098058581352234},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.5006942749023438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4814959764480591},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.4671193063259125},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46444255113601685},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4529981017112732},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.34131765365600586},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.25145256519317627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24649971723556519},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23899221420288086},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13575831055641174},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04797312617301941}],"concepts":[{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.8394513130187988},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6087909936904907},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5318925380706787},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5281493663787842},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5197089314460754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5127471685409546},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5098058581352234},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.5006942749023438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4814959764480591},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.4671193063259125},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46444255113601685},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4529981017112732},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.34131765365600586},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.25145256519317627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24649971723556519},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23899221420288086},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13575831055641174},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04797312617301941}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1354714","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1354714","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5146864000","display_name":null,"funder_award_id":"MOE2017-T2-2-144","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1970611947","https://openalex.org/W1999174665","https://openalex.org/W2048594685","https://openalex.org/W2051344283","https://openalex.org/W2066012686","https://openalex.org/W2072282162","https://openalex.org/W2079884585","https://openalex.org/W2083754610","https://openalex.org/W2136037939","https://openalex.org/W2149498546","https://openalex.org/W2275145915","https://openalex.org/W2462335633","https://openalex.org/W2603909564","https://openalex.org/W2759608098","https://openalex.org/W2950467927","https://openalex.org/W2952020389","https://openalex.org/W3099212336"],"related_works":["https://openalex.org/W4226314133","https://openalex.org/W2305965628","https://openalex.org/W3098348269","https://openalex.org/W3192708935","https://openalex.org/W3186706744","https://openalex.org/W4248057375","https://openalex.org/W2974901631","https://openalex.org/W227870709","https://openalex.org/W2959831473","https://openalex.org/W2007883828"],"abstract_inverted_index":{"We":[0,166],"analyze":[1],"the":[2,14,65,81,84,108,136,140,154,169,186,190,211,221,230,235,255,266,303,315],"convergence":[3,36,132,225],"of":[4,17,64,80,83,117,135,177,179,216,234,265,328,334],"a":[5,28,40,98,112],"multilevel":[6,35,91],"Markov":[7,143],"chain":[8,144],"Monte":[9,145],"Carlo":[10,146],"(MLMCMC)":[11],"algorithm":[12,172],"for":[13,20,39,46,254,270],"Bayesian":[15,175,304],"estimation":[16],"solution":[18],"functionals":[19],"linear,":[21],"parabolic":[22,66],"partial":[23],"differential":[24],"equations":[25],"subject":[26],"to":[27,51,70,182,205,295,314,331],"log-Gaussian":[29,42],"uncertain":[30],"diffusion":[31,43],"coefficient.":[32],"Precisely,":[33],"our":[34,151,329],"analysis":[37,152,226,330],"is":[38,68,97,227,261,293,336],"time-independent,":[41],"coefficient":[44],"and":[45,95,111,124,127,139,195,246,282,298,320],"observations":[47],"which":[48,200,207,260],"are":[49,323],"assumed":[50,69],"be":[52,71],"corrupted":[53],"by":[54,150],"additive,":[55],"centered,":[56],"Gaussian":[57,86,316],"observation":[58],"noise.":[59],"The":[60,89,142],"elliptic":[61,257,271],"spatial":[62,109,137],"part":[63],"PDE":[67],"neither":[72],"uniformly":[73,76],"coercive":[74],"nor":[75],"bounded":[77],"in":[78,93,107,129,133,185,197,239,276,302,325],"terms":[79,134,206],"realizations":[82],"unknown":[85],"random":[87],"field.":[88],"pathwise,":[90],"discretization":[92,187,193,212,310],"space":[94],"time":[96],"standard,":[99],"first":[100,113,130,183,238],"order,":[101,114],"Lagrangian":[102],"simplicial":[103],"finite":[104],"element":[105],"method":[106,268],"domain":[110],"implicit":[115],"timestepping":[116],"backward":[118],"Euler":[119],"type":[120],"ensuring":[121],"good":[122],"dissipation":[123],"unconditional":[125],"stability,":[126],"resulting":[128],"order":[131,184],"meshwidth":[138,194],"timestep.":[141],"(MCMC)":[147],"algorithms":[148],"covered":[149],"comprise":[153],"standard":[155],"independence":[156,319],"sampler":[157],"as":[158,160,164,214],"well":[159],"various":[161],"variants,":[162],"such":[163],"pCN.":[165],"prove":[167],"that":[168,215],"proposed":[170],"MLMCMC":[171,267],"delivers":[173],"approximate":[174],"estimates":[176],"quantities":[178],"interest":[180],"consistent":[181],"parameter":[188],"on":[189,210,220,229],"finest":[191,222],"spatial/temporal":[192],"stepsize":[196],"overall":[198],"work":[199],"scales":[201],"essentially":[202],"(i.e.,":[203],"up":[204],"depend":[208],"logarithmically":[209],"parameters)":[213],"one":[217],"deterministic":[218],"solve":[219],"mesh.":[223],"Our":[224],"based":[228],"discretization-level":[231],"dependent":[232],"truncation":[233],"increments,":[236],"introduced":[237],"[V.":[240,277],"H.":[241,244,278],"Hoang,":[242,279],"J.":[243],"Quek,":[245],"Ch.":[247,280],"Schwab,":[248,281],"Inverse":[249,286],"Problems,":[250,287],"36":[251],"(2020),":[252],"035021]":[253],"corresponding":[256],"forward":[258],"problems,":[259],"an":[262],"essential":[263],"modification":[264,292],"developed":[269],"problems":[272],"under":[273],"uniform":[274],"prior":[275],"A.":[283],"M.":[284],"Stuart,":[285],"29":[288],"(2013),":[289],"085010].":[290],"This":[291],"required":[294],"address":[296],"measurability":[297],"integrability":[299],"issues":[300],"encountered":[301],"posterior":[305],"density":[306],"evaluated":[307],"at":[308],"consecutive":[309],"levels":[311],"with":[312],"respect":[313],"prior.":[317],"Both":[318],"pCN":[321],"samplers":[322],"analyzed":[324],"detail.":[326],"Applicability":[327],"other":[332],"versions":[333],"MCMC":[335],"discussed.":[337]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}