{"id":"https://openalex.org/W2743985642","doi":"https://doi.org/10.1007/s10915-018-00903-0","title":"On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations","display_name":"On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations","publication_year":2019,"publication_date":"2019-03-07","ids":{"openalex":"https://openalex.org/W2743985642","doi":"https://doi.org/10.1007/s10915-018-00903-0","mag":"2743985642"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-00903-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-00903-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-00903-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-00903-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071854504","display_name":"E Weinan","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weinan E","raw_affiliation_strings":["Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030623220","display_name":"Martin Hutzenthaler","orcid":"https://orcid.org/0000-0003-0738-8717"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Hutzenthaler","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen, 45117, Essen, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, 45117, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074382323","display_name":"Arnulf Jentzen","orcid":"https://orcid.org/0000-0002-9840-3339"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Arnulf Jentzen","raw_affiliation_strings":["Seminar f\u00fcr Angewandte Mathematik, ETH Zurich, 8092, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Seminar f\u00fcr Angewandte Mathematik, ETH Zurich, 8092, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036131671","display_name":"Thomas Kruse","orcid":"https://orcid.org/0000-0003-2388-3929"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Kruse","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen, 45117, Essen, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, 45117, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074382323"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":21.1322,"has_fulltext":true,"cited_by_count":133,"citation_normalized_percentile":{"value":0.99619092,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"79","issue":"3","first_page":"1534","last_page":"1571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9116904735565186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7469032406806946},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.6058456897735596},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5736697912216187},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.5377841591835022},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4970860779285431},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4628647267818451},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44176143407821655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9116904735565186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7469032406806946},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.6058456897735596},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5736697912216187},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.5377841591835022},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4970860779285431},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4628647267818451},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44176143407821655},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-018-00903-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-00903-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-00903-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1708.03223","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.03223","pdf_url":"https://arxiv.org/pdf/1708.03223","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:10.1007/s10915-018-00903-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-018-00903-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-018-00903-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1228813458","display_name":null,"funder_award_id":"4-13-1-","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2811237814","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3254747768","display_name":null,"funder_award_id":"HU 1889/6-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4239678208","display_name":null,"funder_award_id":"ONR N00014-13-1-0338","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4296360068","display_name":null,"funder_award_id":"ONR N00014-13-1-0338","funder_id":"https://openalex.org/F4320338298","funder_display_name":"Office of Naval Research Global"},{"id":"https://openalex.org/G4776870722","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5403500396","display_name":null,"funder_award_id":"DE-SC0009248","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6388601012","display_name":null,"funder_award_id":"N00014-13-1-0338","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G6743243744","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7914223327","display_name":null,"funder_award_id":"DOE DE-SC0009248","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338298","display_name":"Office of Naval Research Global","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2743985642.pdf","grobid_xml":"https://content.openalex.org/works/W2743985642.grobid-xml"},"referenced_works_count":112,"referenced_works":["https://openalex.org/W94839203","https://openalex.org/W99776242","https://openalex.org/W609699901","https://openalex.org/W1484867920","https://openalex.org/W1513085673","https://openalex.org/W1575104486","https://openalex.org/W1582218176","https://openalex.org/W1606518485","https://openalex.org/W1740091825","https://openalex.org/W1811405573","https://openalex.org/W1835030294","https://openalex.org/W1948872067","https://openalex.org/W1969732258","https://openalex.org/W1975076156","https://openalex.org/W1977646979","https://openalex.org/W1978546215","https://openalex.org/W1978577723","https://openalex.org/W1981041832","https://openalex.org/W1981151146","https://openalex.org/W1982008399","https://openalex.org/W1983286604","https://openalex.org/W1984865765","https://openalex.org/W1994791309","https://openalex.org/W1998562371","https://openalex.org/W1999483367","https://openalex.org/W2004794023","https://openalex.org/W2004973016","https://openalex.org/W2007567546","https://openalex.org/W2008534422","https://openalex.org/W2012371480","https://openalex.org/W2022684404","https://openalex.org/W2025559620","https://openalex.org/W2027654260","https://openalex.org/W2028811441","https://openalex.org/W2031382602","https://openalex.org/W2034548366","https://openalex.org/W2036709538","https://openalex.org/W2038078026","https://openalex.org/W2039366144","https://openalex.org/W2039546575","https://openalex.org/W2040007132","https://openalex.org/W2040378705","https://openalex.org/W2043281212","https://openalex.org/W2044203216","https://openalex.org/W2046331573","https://openalex.org/W2046564207","https://openalex.org/W2046606859","https://openalex.org/W2048370823","https://openalex.org/W2050871708","https://openalex.org/W2051031503","https://openalex.org/W2052852643","https://openalex.org/W2072373192","https://openalex.org/W2073001881","https://openalex.org/W2074451409","https://openalex.org/W2075910419","https://openalex.org/W2077048879","https://openalex.org/W2078895915","https://openalex.org/W2082621526","https://openalex.org/W2083017901","https://openalex.org/W2092943197","https://openalex.org/W2095445700","https://openalex.org/W2117358914","https://openalex.org/W2118587148","https://openalex.org/W2124948346","https://openalex.org/W2126800238","https://openalex.org/W2129289929","https://openalex.org/W2137519698","https://openalex.org/W2146267297","https://openalex.org/W2148965913","https://openalex.org/W2157883119","https://openalex.org/W2161836471","https://openalex.org/W2163715525","https://openalex.org/W2164282683","https://openalex.org/W2164907988","https://openalex.org/W2167018969","https://openalex.org/W2169797654","https://openalex.org/W2247836589","https://openalex.org/W2256916148","https://openalex.org/W2293641753","https://openalex.org/W2318465330","https://openalex.org/W2514876979","https://openalex.org/W2556342349","https://openalex.org/W2581605984","https://openalex.org/W2608271650","https://openalex.org/W2751918446","https://openalex.org/W2918085900","https://openalex.org/W2950353647","https://openalex.org/W2950427768","https://openalex.org/W2951662467","https://openalex.org/W2964242874","https://openalex.org/W2983583895","https://openalex.org/W3013068944","https://openalex.org/W3025390840","https://openalex.org/W3100801504","https://openalex.org/W3101215572","https://openalex.org/W3101256565","https://openalex.org/W3101471540","https://openalex.org/W3101608030","https://openalex.org/W3103392198","https://openalex.org/W3106010402","https://openalex.org/W3121352784","https://openalex.org/W3121492042","https://openalex.org/W3123910813","https://openalex.org/W3124749042","https://openalex.org/W3124855974","https://openalex.org/W4231021340","https://openalex.org/W4240828289","https://openalex.org/W4242273588","https://openalex.org/W4250934876","https://openalex.org/W4252168909","https://openalex.org/W4289438379","https://openalex.org/W4324396040"],"related_works":["https://openalex.org/W2006263304","https://openalex.org/W2155548976","https://openalex.org/W1972240278","https://openalex.org/W1967450583","https://openalex.org/W2735510078","https://openalex.org/W3020098708","https://openalex.org/W2482000553","https://openalex.org/W3023046551","https://openalex.org/W184885699","https://openalex.org/W2070051820"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2017-08-17T00:00:00"}