{"id":"https://openalex.org/W1278301499","doi":"https://doi.org/10.1137/140990036","title":"A Posteriori Error Estimates for the Solution of Variational Inverse Problems","display_name":"A Posteriori Error Estimates for the Solution of Variational Inverse Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1278301499","doi":"https://doi.org/10.1137/140990036","mag":"1278301499"},"language":"en","primary_location":{"id":"doi:10.1137/140990036","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140990036","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/A5082476958","display_name":"Vishwas Rao","orcid":"https://orcid.org/0000-0002-4395-6075"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vishwas Rao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008436217","display_name":"Adrian Sandu","orcid":"https://orcid.org/0000-0002-5380-0103"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adrian Sandu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082476958"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8174,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.93093594,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"737","last_page":"761"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983000159263611,"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":0.9983000159263611,"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6923940181732178},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.6677736043930054},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6649428606033325},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.59367436170578},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5439903140068054},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4986593723297119},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48792049288749695},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4803144335746765},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.4716357886791229},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42703524231910706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38383007049560547},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38267141580581665},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10583847761154175},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0994313657283783}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6923940181732178},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.6677736043930054},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6649428606033325},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.59367436170578},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5439903140068054},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4986593723297119},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48792049288749695},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4803144335746765},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.4716357886791229},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42703524231910706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38383007049560547},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38267141580581665},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10583847761154175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0994313657283783},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140990036","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140990036","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":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1988046761","https://openalex.org/W1988168526","https://openalex.org/W1990835110","https://openalex.org/W2004431879","https://openalex.org/W2017865929","https://openalex.org/W2020132470","https://openalex.org/W2025946447","https://openalex.org/W2026467797","https://openalex.org/W2063660782","https://openalex.org/W2067120476","https://openalex.org/W2077149349","https://openalex.org/W2078882674","https://openalex.org/W2079159741","https://openalex.org/W2081416965","https://openalex.org/W2088901180","https://openalex.org/W2105993603","https://openalex.org/W2133147107","https://openalex.org/W2141069969","https://openalex.org/W2151325878","https://openalex.org/W2152111295","https://openalex.org/W2167539472","https://openalex.org/W2168175751","https://openalex.org/W2338755529"],"related_works":["https://openalex.org/W2654527859","https://openalex.org/W1666666856","https://openalex.org/W1974056099","https://openalex.org/W2276167504","https://openalex.org/W1991093342","https://openalex.org/W2386077341","https://openalex.org/W1974424152","https://openalex.org/W3155039083","https://openalex.org/W1543136835","https://openalex.org/W4210375670"],"abstract_inverted_index":{"Dynamically":[0],"data-driven":[1],"application":[2],"systems":[3,80],"integrate":[4],"computational":[5,49,97],"simulations":[6],"and":[7,47,85,102,144,168],"physical":[8,38],"measurements":[9,24,46],"in":[10,18,43,134,141,153,165],"a":[11,27,37,58,87,108,114,123,129],"symbiotic":[12],"feedback":[13],"control":[14],"system.":[15],"Inverse":[16],"problems":[17],"this":[19],"framework":[20],"use":[21,158],"data":[22,94],"from":[23],"along":[25],"with":[26,148],"numerical":[28],"model":[29,50,143],"to":[30,52,60],"estimate":[31,61],"the":[32,45,48,62,68,111,119,135,139,142,149,157,160],"parameters":[33],"or":[34],"state":[35],"of":[36,40,64,71,90,132,159],"system":[39],"interest.":[41],"Uncertainties":[42],"both":[44,166],"lead":[51],"inaccurate":[53],"estimates.":[54],"This":[55],"work":[56],"develops":[57],"methodology":[59,112],"impact":[63],"different":[65],"errors":[66],"on":[67,77,86],"variational":[69],"solutions":[70],"inverse":[72,91,120,136],"problems.":[73],"The":[74,96],"focus":[75],"is":[76],"time":[78],"evolving":[79],"described":[81],"by":[82],"differential":[83],"equations,":[84],"particular":[88],"class":[89],"problems,":[92],"namely,":[93],"assimilation.":[95],"algorithm":[98],"uses":[99],"first":[100],"order":[101,104],"second":[103],"adjoint":[105],"models.":[106],"In":[107,122],"deterministic":[109,167],"setting":[110,125],"provides":[113,127],"posteriori":[115,130],"error":[116,162],"estimates":[117],"for":[118],"solution.":[121],"probabilistic":[124,169],"it":[126],"an":[128],"quantification":[131],"uncertainty":[133],"solution,":[137],"given":[138],"uncertainties":[140],"data.":[145],"Numerical":[146],"experiments":[147],"shallow":[150],"water":[151],"equations":[152],"spherical":[154],"coordinates":[155],"illustrate":[156],"proposed":[161],"estimation":[163],"machinery":[164],"settings.":[170]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}