{"id":"https://openalex.org/W3107254801","doi":"https://doi.org/10.1137/19m1295222","title":"Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds","display_name":"Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3107254801","doi":"https://doi.org/10.1137/19m1295222","mag":"3107254801"},"language":"en","primary_location":{"id":"doi:10.1137/19m1295222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1295222","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/A5112564733","display_name":"John Harlim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John Harlim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089991960","display_name":"Daniel Sanz-Alonso","orcid":"https://orcid.org/0000-0002-5022-864X"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Sanz-Alonso","raw_affiliation_strings":["The University of Chicago,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Chicago,","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025921204","display_name":"Ruiyi Yang","orcid":"https://orcid.org/0000-0002-0179-6165"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ruiyi Yang","raw_affiliation_strings":["The University of Chicago,"],"raw_orcid":"https://orcid.org/0000-0002-0179-6165","affiliations":[{"raw_affiliation_string":"The University of Chicago,","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112564733"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3589,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.85725361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"8","issue":"4","first_page":"1414","last_page":"1445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9970999956130981,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9940000176429749,"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":0.9914000034332275,"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/elliptic-operator","display_name":"Elliptic operator","score":0.668289840221405},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6647709012031555},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5392774939537048},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5389043092727661},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5245252847671509},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.514006495475769},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5088205933570862},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5032684206962585},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5011563301086426},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.49770835041999817},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4288754463195801},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.41848084330558777},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37676912546157837},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3021012544631958},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.15338316559791565},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10848742723464966}],"concepts":[{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.668289840221405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6647709012031555},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5392774939537048},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5389043092727661},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5245252847671509},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.514006495475769},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5088205933570862},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5032684206962585},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5011563301086426},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.49770835041999817},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4288754463195801},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.41848084330558777},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37676912546157837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3021012544631958},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.15338316559791565},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10848742723464966},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1295222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1295222","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/G2482437351","display_name":null,"funder_award_id":"DMS-1854299","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G2740328507","display_name":null,"funder_award_id":"DMS-1912802","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G513865521","display_name":null,"funder_award_id":"DMS-1912818","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G7691849669","display_name":null,"funder_award_id":"DMS-1619661","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1837874438","https://openalex.org/W1966949944","https://openalex.org/W1974228980","https://openalex.org/W1988068819","https://openalex.org/W1998840347","https://openalex.org/W2006554089","https://openalex.org/W2009262561","https://openalex.org/W2033721384","https://openalex.org/W2041865295","https://openalex.org/W2054917359","https://openalex.org/W2055460625","https://openalex.org/W2066880755","https://openalex.org/W2069187442","https://openalex.org/W2072753931","https://openalex.org/W2083691506","https://openalex.org/W2097469960","https://openalex.org/W2131086168","https://openalex.org/W2132914434","https://openalex.org/W2149498546","https://openalex.org/W2151306679","https://openalex.org/W2152657433","https://openalex.org/W2156268854","https://openalex.org/W2157670588","https://openalex.org/W2170429437","https://openalex.org/W2236957706","https://openalex.org/W2550604839","https://openalex.org/W2575742565","https://openalex.org/W2786364421","https://openalex.org/W2891337579","https://openalex.org/W2953988481","https://openalex.org/W2962768516","https://openalex.org/W2962963464","https://openalex.org/W2963122501","https://openalex.org/W2963266525","https://openalex.org/W2963371806","https://openalex.org/W2963561100","https://openalex.org/W2963687408","https://openalex.org/W2964203384","https://openalex.org/W2964290469","https://openalex.org/W2968350215","https://openalex.org/W3021293439","https://openalex.org/W3103444582","https://openalex.org/W4213367101"],"related_works":["https://openalex.org/W2546668543","https://openalex.org/W3199909384","https://openalex.org/W3086626333","https://openalex.org/W3201820274","https://openalex.org/W4205953005","https://openalex.org/W4247773374","https://openalex.org/W2370767228","https://openalex.org/W2024754535","https://openalex.org/W2007011975","https://openalex.org/W2790094106"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,26,31,47,56,75,96,115,124,129,138,146,149],"formulation":[4],"and":[5,84,88,118,132],"implementation":[6],"of":[7,15,29,34,46,95,104,148],"Bayesian":[8,112],"inverse":[9,27,116],"problems":[10],"to":[11,74,86,114],"learn":[12],"input":[13],"parameters":[14],"partial":[16],"differential":[17,58],"equations":[18],"(PDEs)":[19],"defined":[20,136],"on":[21,39,123],"manifolds.":[22],"Specifically,":[23],"we":[24,54],"study":[25],"problem":[28],"determining":[30],"diffusion":[32],"coefficient":[33],"a":[35,40,61,101,111],"second-order":[36],"elliptic":[37,57],"PDE":[38],"closed":[41],"manifold":[42,51,105],"from":[43],"noisy":[44],"measurements":[45],"solution.":[48],"Inspired":[49],"by":[50],"learning":[52],"techniques,":[53],"approximate":[55,134],"operator":[59,64],"with":[60,137],"kernel-based":[62],"integral":[63],"that":[65,100],"can":[66,89],"be":[67,90],"discretized":[68],"via":[69],"Monte":[70],"Carlo":[71],"without":[72,92],"reference":[73],"Riemannian":[76],"metric.":[77],"The":[78],"resulting":[79],"computational":[80],"method":[81],"is":[82,107],"mesh-free":[83],"easy":[85],"implement,":[87],"applied":[91],"full":[93],"knowledge":[94],"underlying":[97],"manifold,":[98],"provided":[99],"point":[102],"cloud":[103],"samples":[106],"available.":[108],"We":[109],"adopt":[110],"perspective":[113],"problem,":[117],"establish":[119],"an":[120,133],"upper":[121],"bound":[122],"total":[125],"variation":[126],"distance":[127],"between":[128],"true":[130],"posterior":[131,135],"kernel":[139],"forward":[140],"map.":[141],"Supporting":[142],"numerical":[143],"results":[144],"show":[145],"effectiveness":[147],"proposed":[150],"methodology.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}