{"id":"https://openalex.org/W2594400676","doi":"https://doi.org/10.1137/17m1139357","title":"Bayesian Probabilistic Numerical Methods","display_name":"Bayesian Probabilistic Numerical Methods","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2594400676","doi":"https://doi.org/10.1137/17m1139357","mag":"2594400676"},"language":"en","primary_location":{"id":"doi:10.1137/17m1139357","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1139357","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1139357","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1139357","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jon Cockayne","orcid":null},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jon Cockayne","raw_affiliation_strings":["Department of Statistics, University of Warwick, Coventry CV4 7AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Warwick, Coventry CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Chris J. Oates","orcid":null},"institutions":[{"id":"https://openalex.org/I125680101","display_name":"Turing Institute","ror":"https://ror.org/02x2mw849","country_code":"GB","type":"facility","lineage":["https://openalex.org/I125680101"]},{"id":"https://openalex.org/I2800016483","display_name":"British Library","ror":"https://ror.org/05dhe8b71","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2800016483"]},{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chris J. Oates","raw_affiliation_strings":["Alan Turing Institute, British Library, London NW1 2DB, UK","School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK, and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alan Turing Institute, British Library, London NW1 2DB, UK","institution_ids":["https://openalex.org/I125680101","https://openalex.org/I2800016483"]},{"raw_affiliation_string":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK, and","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"middle","author":{"id":null,"display_name":"T. J. Sullivan","orcid":null},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. J. Sullivan","raw_affiliation_strings":["Freie Universitt Berlin, Berlin 14195, Germany, and","Zuse Institute Berlin, Berlin 14195, Ger-many"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Freie Universitt Berlin, Berlin 14195, Germany, and","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Zuse Institute Berlin, Berlin 14195, Ger-many","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mark Girolami","orcid":null},"institutions":[{"id":"https://openalex.org/I125680101","display_name":"Turing Institute","ror":"https://ror.org/02x2mw849","country_code":"GB","type":"facility","lineage":["https://openalex.org/I125680101"]},{"id":"https://openalex.org/I2800016483","display_name":"British Library","ror":"https://ror.org/05dhe8b71","country_code":"GB","type":"archive","lineage":["https://openalex.org/I2800016483"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mark Girolami","raw_affiliation_strings":["Alan Turing Institute, British Library, London NW1 2DB, UK","Department of Mathematics, Imperial College London, London SW7 2AZ, UK, and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alan Turing Institute, British Library, London NW1 2DB, UK","institution_ids":["https://openalex.org/I125680101","https://openalex.org/I2800016483"]},{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London SW7 2AZ, UK, and","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2181,"has_fulltext":true,"cited_by_count":81,"citation_normalized_percentile":{"value":0.97012137,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"61","issue":"3","first_page":"756","last_page":"789"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.48730000853538513,"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"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.48730000853538513,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.23190000653266907,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.17640000581741333,"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/numerical-analysis","display_name":"Numerical analysis","score":0.7091000080108643},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.698199987411499},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5928000211715698},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4618000090122223},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4368000030517578},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.415800005197525},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.40619999170303345},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.3720000088214874}],"concepts":[{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.7091000080108643},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.698199987411499},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5928000211715698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47850000858306885},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46129998564720154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4571000039577484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4410000145435333},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4097000062465668},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.40619999170303345},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.32170000672340393},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.30959999561309814},{"id":"https://openalex.org/C154181440","wikidata":"https://www.wikidata.org/wiki/Q1683292","display_name":"Numerical differentiation","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C60782215","wikidata":"https://www.wikidata.org/wiki/Q3333679","display_name":"Probabilistic method","level":3,"score":0.25690001249313354}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1139357","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1139357","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1139357","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:482225","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1702.03673","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.03673","pdf_url":"https://arxiv.org/pdf/1702.03673","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":"doi:10.1137/17m1139357","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1139357","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1139357","source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1322834978","display_name":"Inference, COmputation and Numerics for Insights into Cities (ICONIC)","funder_award_id":"EP/P020720/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1774196161","display_name":null,"funder_award_id":"1127914","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G1818326008","display_name":"Semantic Information Pursuit for Multimodal Data Analysis","funder_award_id":"EP/R018413/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1871434800","display_name":null,"funder_award_id":"EP/R034710/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1935751110","display_name":null,"funder_award_id":"EP/P020720/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1962099758","display_name":null,"funder_award_id":"EP/J016934/3","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G290511076","display_name":"Advancing the Geometric Framework for Computational Statistics: Theory, Methodology and Modern Day Applications","funder_award_id":"EP/J016934/3","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2972334111","display_name":null,"funder_award_id":"EP/R034710/1","funder_id":"https://openalex.org/F4320320005","funder_display_name":"Royal Academy of Engineering"},{"id":"https://openalex.org/G3179926582","display_name":"Delivering Enhanced Through-Life Nuclear Asset Management","funder_award_id":"EP/R004889/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3690003352","display_name":null,"funder_award_id":"EP/R004889","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4062695751","display_name":null,"funder_award_id":"EP/R004889/1","funder_id":"https://openalex.org/F4320320005","funder_display_name":"Royal Academy of Engineering"},{"id":"https://openalex.org/G4123259794","display_name":null,"funder_award_id":"1127914","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4317490300","display_name":null,"funder_award_id":"EP/R018413/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4412212456","display_name":null,"funder_award_id":"EP/R018413/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6678195701","display_name":null,"funder_award_id":"EP/P020720/2","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8280225390","display_name":null,"funder_award_id":"DMS-1127914","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8492689677","display_name":null,"funder_award_id":"DMS-1127914","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G926698369","display_name":null,"funder_award_id":"R034710","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G965103402","display_name":"CoSInES (COmputational Statistical INference for Engineering and Security)","funder_award_id":"EP/R034710/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310833","display_name":"Lloyd's Register Foundation","ror":"https://ror.org/057q4mw47"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320320005","display_name":"Royal Academy of Engineering","ror":"https://ror.org/0526snb40"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324521","display_name":"Freie Universit\u00e4t Berlin","ror":null},{"id":"https://openalex.org/F4320325699","display_name":"Lloyd's Register","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2594400676.pdf","grobid_xml":"https://content.openalex.org/works/W2594400676.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W112187595","https://openalex.org/W1545319692","https://openalex.org/W1818848341","https://openalex.org/W1856502440","https://openalex.org/W1971615387","https://openalex.org/W1976044168","https://openalex.org/W1979258129","https://openalex.org/W1984693296","https://openalex.org/W1986823579","https://openalex.org/W1996397859","https://openalex.org/W1997497293","https://openalex.org/W2001102637","https://openalex.org/W2003706076","https://openalex.org/W2018044188","https://openalex.org/W2024689619","https://openalex.org/W2027915600","https://openalex.org/W2046667530","https://openalex.org/W2053635157","https://openalex.org/W2060229389","https://openalex.org/W2068251904","https://openalex.org/W2072403451","https://openalex.org/W2107940303","https://openalex.org/W2110720940","https://openalex.org/W2135267747","https://openalex.org/W2146443948","https://openalex.org/W2149498546","https://openalex.org/W2165429502","https://openalex.org/W2226273852","https://openalex.org/W2243651912","https://openalex.org/W2328111639","https://openalex.org/W2404700421","https://openalex.org/W2467245180","https://openalex.org/W2534928453","https://openalex.org/W2605229807","https://openalex.org/W2790234460","https://openalex.org/W2903833540","https://openalex.org/W2911546748","https://openalex.org/W2962738342","https://openalex.org/W2962828807","https://openalex.org/W2963082475","https://openalex.org/W2963135308","https://openalex.org/W2963462656","https://openalex.org/W2963634130","https://openalex.org/W2963777151","https://openalex.org/W2964051671","https://openalex.org/W3098369825","https://openalex.org/W4249128886"],"related_works":[],"abstract_inverted_index":{"Over":[0],"forty":[1],"years":[2],"ago":[3],"average-case":[4],"error":[5],"was":[6],"proposed":[7,116],"in":[8],"the":[9,32,58,78,82,103,151],"applied":[10],"mathematics":[11],"literature":[12],"as":[13,70],"an":[14,146],"alternative":[15],"criterion":[16,29],"with":[17,55],"which":[18,93],"to":[19,25,57,72,88,127,137],"assess":[20],"numerical":[21,40,43,68,79,96,112,133,141,154],"methods.":[22],"In":[23],"contrast":[24],"worst-case":[26],"error,":[27],"this":[28],"relies":[30],"on":[31,48],"construction":[33],"of":[34,129,153],"a":[35,111,160],"probability":[36],"measure":[37],"over":[38,52],"candidate":[39],"tasks,":[41],"and":[42,64,105,117,156,159],"methods":[44,69,97,134],"are":[45,98,135],"assessed":[46],"based":[47,76],"their":[49],"average":[50],"performance":[51],"those":[53],"tasks":[54],"respect":[56],"measure.":[59],"This":[60,85],"paper":[61],"goes":[62],"further":[63],"establishes":[65],"Bayesian":[66,83,94],"probabilistic":[67,95,132],"solutions":[71],"certain":[73],"inverse":[74],"problems":[75],"upon":[77],"task":[80],"within":[81],"framework.":[84],"allows":[86],"us":[87],"establish":[89],"general":[90,109],"conditions":[91],"under":[92],"well":[99],"defined,":[100],"encompassing":[101],"both":[102],"nonlinear":[104],"non-Gaussian":[106],"contexts.":[107],"For":[108],"computation,":[110,130],"approximation":[113],"scheme":[114],"is":[115,125,164],"its":[118],"asymptotic":[119],"convergence":[120],"established.":[121],"The":[122,143],"theoretical":[123],"development":[124],"extended":[126],"pipelines":[128],"wherein":[131],"composed":[136],"solve":[138],"more":[139],"challenging":[140,161],"tasks.":[142],"contribution":[144],"highlights":[145],"important":[147],"research":[148],"frontier":[149],"at":[150],"interface":[152],"analysis":[155],"uncertainty":[157],"quantification,":[158],"industrial":[162],"application":[163],"presented.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-03-16T00:00:00"}