{"id":"https://openalex.org/W3045687008","doi":"https://doi.org/10.2140/camcos.2021.16.181","title":"Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis","display_name":"Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis","publication_year":2021,"publication_date":"2021-11-02","ids":{"openalex":"https://openalex.org/W3045687008","doi":"https://doi.org/10.2140/camcos.2021.16.181","mag":"3045687008"},"language":"en","primary_location":{"id":"doi:10.2140/camcos.2021.16.181","doi":"https://doi.org/10.2140/camcos.2021.16.181","is_oa":false,"landing_page_url":"https://doi.org/10.2140/camcos.2021.16.181","pdf_url":null,"source":{"id":"https://openalex.org/S4210211657","display_name":"Communications in Applied Mathematics and Computational Science","issn_l":"1559-3940","issn":["1559-3940","2157-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Applied Mathematics and Computational Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2007.13930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032805069","display_name":"Shanyin Tong","orcid":"https://orcid.org/0000-0001-5447-0233","observed_orcids":["https://orcid.org/0000-0001-5447-0233"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shanyin Tong","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York City, NY, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York City, NY, United States","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044193587","display_name":"Eric Vanden\u2010Eijnden","orcid":"https://orcid.org/0000-0001-7982-5854","observed_orcids":["https://orcid.org/0000-0001-7982-5854"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Vanden-Eijnden","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY, United States","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012373865","display_name":"Georg Stadler","orcid":"https://orcid.org/0000-0001-7762-6544","observed_orcids":["https://orcid.org/0000-0001-7762-6544","https://orcid.org/0000-0002-4080-122X"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Georg Stadler","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York City, NY, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York City, NY, United States","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7453,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.92338863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"16","issue":"2","first_page":"181","last_page":"225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.5922999978065491,"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":0.5922999978065491,"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/T14146","display_name":"Earthquake and Tsunami Effects","score":0.05130000039935112,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.026599999517202377,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extreme-event-probability","display_name":"extreme event probability","score":0.8050000071525574},{"id":"https://openalex.org/keywords/large-deviations","display_name":"large deviations","score":0.972000002861023},{"id":"https://openalex.org/keywords/pde-constrained-optimization","display_name":"PDE-constrained optimization","score":0.9279999732971191},{"id":"https://openalex.org/keywords/random-parameters","display_name":"random coefficients","score":0.6119999885559082},{"id":"https://openalex.org/keywords/adjoint-method","display_name":"adjoint method","score":0.8730000257492065},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"importance sampling","score":0.9800000190734863},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"shallow water equations","score":0.824999988079071},{"id":"https://openalex.org/keywords/tsunami","display_name":"tsunami","score":0.5210000276565552},{"id":"https://openalex.org/keywords/earthquake-induced-tsunamis","display_name":"earthquake-induced tsunamis","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.5543587803840637},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.530127227306366},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.5245832800865173},{"id":"https://openalex.org/C2777317252","wikidata":"https://www.wikidata.org/wiki/Q18393516","display_name":"Rare events","level":2,"score":0.49628835916519165},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.48501917719841003},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.47324901819229126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47076109051704407},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46385857462882996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45156314969062805},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.45130738615989685},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.44867751002311707},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4485430419445038},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4462234675884247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3738240599632263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35706907510757446},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19193679094314575},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12984374165534973},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2140/camcos.2021.16.181","doi":"https://doi.org/10.2140/camcos.2021.16.181","is_oa":false,"landing_page_url":"https://doi.org/10.2140/camcos.2021.16.181","pdf_url":null,"source":{"id":"https://openalex.org/S4210211657","display_name":"Communications in Applied Mathematics and Computational Science","issn_l":"1559-3940","issn":["1559-3940","2157-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320446","host_organization_name":"Mathematical Sciences Publishers","host_organization_lineage":["https://openalex.org/P4310320446"],"host_organization_lineage_names":["Mathematical Sciences Publishers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Applied Mathematics and Computational Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.13930","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.13930","pdf_url":"https://arxiv.org/pdf/2007.13930","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"mag:3045687008","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2007.13930.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.13930","doi":"https://doi.org/10.48550/arxiv.2007.13930","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.13930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.13930","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.13930","pdf_url":"https://arxiv.org/pdf/2007.13930","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W93748562","https://openalex.org/W105972687","https://openalex.org/W136419697","https://openalex.org/W196710731","https://openalex.org/W232805744","https://openalex.org/W433418221","https://openalex.org/W596189563","https://openalex.org/W629793771","https://openalex.org/W1509146450","https://openalex.org/W1549451790","https://openalex.org/W1555627060","https://openalex.org/W1576267150","https://openalex.org/W1600371943","https://openalex.org/W1621653743","https://openalex.org/W1663653474","https://openalex.org/W1820125862","https://openalex.org/W1963649399","https://openalex.org/W1965777485","https://openalex.org/W1969272920","https://openalex.org/W1980357388","https://openalex.org/W1992188335","https://openalex.org/W1993177346","https://openalex.org/W2000521974","https://openalex.org/W2001605166","https://openalex.org/W2015768906","https://openalex.org/W2030530609","https://openalex.org/W2031291057","https://openalex.org/W2032119807","https://openalex.org/W2036213650","https://openalex.org/W2052242710","https://openalex.org/W2059120410","https://openalex.org/W2063471322","https://openalex.org/W2066593407","https://openalex.org/W2069739265","https://openalex.org/W2080735494","https://openalex.org/W2117756735","https://openalex.org/W2124799255","https://openalex.org/W2289423694","https://openalex.org/W2489524879","https://openalex.org/W2514973904","https://openalex.org/W2605625916","https://openalex.org/W2606860700","https://openalex.org/W2809801739","https://openalex.org/W2884565644","https://openalex.org/W2889471485","https://openalex.org/W2913818203","https://openalex.org/W2954311773","https://openalex.org/W2961792079","https://openalex.org/W2962707560","https://openalex.org/W3003952667","https://openalex.org/W3029645440","https://openalex.org/W4251197584","https://openalex.org/W4253932762","https://openalex.org/W4301258660"],"related_works":["https://openalex.org/W4206414108","https://openalex.org/W2963202249","https://openalex.org/W2796676086","https://openalex.org/W2884023937","https://openalex.org/W3090553373","https://openalex.org/W2620187801","https://openalex.org/W2898653976","https://openalex.org/W2091209586","https://openalex.org/W3015078960","https://openalex.org/W4398230810"],"abstract_inverted_index":{"We":[0,125,163,188,222,237],"propose":[1,127],"and":[2,52,155,166,266],"compare":[3],"methods":[4,78,98,131,175,260],"for":[5,151,261],"the":[6,29,36,44,84,88,101,112,115,144,171,179,182,190,197,215,234,239,249,277],"analysis":[7],"of":[8,35,90,103,114,122,130,143,173,181,192,199,214,251,258,270],"extreme":[9,94,116,145,200,262],"events":[10,117,183,202],"in":[11,21,27],"complex":[12],"systems":[13],"governed":[14],"by":[15,209],"PDEs":[16],"that":[17,31,82,170],"involve":[18],"random":[19,228],"parameters,":[20],"situations":[22],"where":[23],"we":[24,62,184,254],"are":[25,149,158,185,206],"interested":[26,186],"quantifying":[28],"probability":[30,49,198,264],"a":[32,41,128,210,227,256],"scalar":[33],"function":[34,86],"system's":[37],"solution":[38],"is":[39,46,50,56,176],"above":[40],"threshold.":[42],"If":[43],"threshold":[45],"large,":[47],"this":[48,60,104,224,252],"small":[51],"its":[53],"accurate":[54],"estimation":[55],"challenging.":[57],"To":[58],"tackle":[59],"difficulty,":[61],"blend":[63],"theoretical":[64,165],"results":[65],"from":[66,74],"large":[67],"deviation":[68],"theory":[69],"(LDT)":[70],"with":[71],"numerical":[72,167],"tools":[73],"PDE-constrained":[75],"optimization.":[76],"Our":[77],"first":[79],"compute":[80,100],"parameters":[81,91],"minimize":[83],"LDT-rate":[85],"over":[87],"set":[89],"leading":[92],"to":[93,99,132,178,195,244,276],"events,":[95],"using":[96],"adjoint":[97],"gradient":[102],"rate":[105],"function.":[106],"The":[107],"minimizers":[108],"give":[109,164],"information":[110],"about":[111],"mechanism":[113],"as":[118,120,226],"well":[119],"estimates":[121],"their":[123],"probability.":[124],"then":[126],"series":[129],"refine":[133],"these":[134],"estimates,":[135],"either":[136],"via":[137],"importance":[138],"sampling":[139],"or":[140],"geometric":[141],"approximation":[142],"event":[146,263],"sets.":[147],"Results":[148],"formulated":[150],"general":[152],"parameter":[153],"distributions":[154],"detailed":[156],"expressions":[157],"provided":[159],"when":[160],"Gaussian":[161],"distributions.":[162],"arguments":[168],"showing":[169],"performance":[172],"our":[174,193,259],"insensitive":[177],"extremeness":[180],"in.":[187],"illustrate":[189],"application":[191],"approach":[194],"quantify":[196],"tsunami":[201],"on":[203,280],"shore.":[204,281],"Tsunamis":[205],"typically":[207],"caused":[208],"sudden,":[211],"unpredictable":[212],"change":[213,225,274],"ocean":[216,271],"floor":[217,272],"elevation":[218,273],"during":[219],"an":[220],"earthquake.":[221],"model":[223,245],"process,":[229],"which":[230,268],"takes":[231],"into":[232],"account":[233],"underlying":[235],"physics.":[236],"use":[238],"one-dimensional":[240],"shallow":[241],"water":[242],"equation":[243],"tsunamis":[246,279],"numerically.":[247],"In":[248],"context":[250],"example,":[253],"present":[255],"comparison":[257],"estimation,":[265],"find":[267],"type":[269],"leads":[275],"largest":[278]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2020-08-03T00:00:00"}