{"id":"https://openalex.org/W59438544","doi":null,"title":"Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions","display_name":"Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W59438544","mag":"59438544"},"language":"en","primary_location":{"id":"pmh:oai:dukespace.lib.duke.edu:10161/8718","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/8718","pdf_url":"http://hdl.handle.net/10161/8718","source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dissertation"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10161/8718","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017471297","display_name":"Miles Crosskey","orcid":"https://orcid.org/0000-0002-0625-7718","observed_orcids":["https://orcid.org/0000-0002-0625-7718"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miles Crosskey","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0625-7718","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017471297"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9634000062942505,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9634000062942505,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.03310000151395798,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"unsupervised learning","score":0.8090000152587891},{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.8180000185966492},{"id":"https://openalex.org/keywords/timescale-separation","display_name":"time-scale separation","score":0.8399999737739563},{"id":"https://openalex.org/keywords/fast-simulation","display_name":"fast simulation","score":0.36500000953674316}],"concepts":[{"id":"https://openalex.org/C2776673561","wikidata":"https://www.wikidata.org/wiki/Q655357","display_name":"Atlas (anatomy)","level":2,"score":0.7899067997932434},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5138300061225891},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49201270937919617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41992273926734924},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29588717222213745},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2522232234477997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25090184807777405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21312710642814636},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.07150956988334656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:dukespace.lib.duke.edu:10161/8718","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/8718","pdf_url":"http://hdl.handle.net/10161/8718","source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dissertation"},{"id":"mag:59438544","doi":null,"is_oa":false,"landing_page_url":"https://dukespace.lib.duke.edu/dspace/bitstream/10161/8718/1/Crosskey_duke_0066D_12350.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:dukespace.lib.duke.edu:10161/8718","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/8718","pdf_url":"http://hdl.handle.net/10161/8718","source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Dissertation"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W59438544.pdf","grobid_xml":"https://content.openalex.org/works/W59438544.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1390923","https://openalex.org/W1519654970","https://openalex.org/W1524094700","https://openalex.org/W1530927473","https://openalex.org/W1547249381","https://openalex.org/W1556269498","https://openalex.org/W1562856242","https://openalex.org/W1572902284","https://openalex.org/W1590943005","https://openalex.org/W1595132914","https://openalex.org/W1673352269","https://openalex.org/W1852328762","https://openalex.org/W1964529687","https://openalex.org/W1970592267","https://openalex.org/W1971725855","https://openalex.org/W1987236926","https://openalex.org/W2021270935","https://openalex.org/W2032227660","https://openalex.org/W2053348581","https://openalex.org/W2063532964","https://openalex.org/W2064556178","https://openalex.org/W2064733273","https://openalex.org/W2070460788","https://openalex.org/W2090658476","https://openalex.org/W2092709451","https://openalex.org/W2096450582","https://openalex.org/W2112148214","https://openalex.org/W2131172946","https://openalex.org/W2133296809","https://openalex.org/W2139139723","https://openalex.org/W2160341881","https://openalex.org/W2167077362","https://openalex.org/W2227023074","https://openalex.org/W2229640315","https://openalex.org/W2405566609","https://openalex.org/W3099404592","https://openalex.org/W3124025666"],"related_works":["https://openalex.org/W7100142974","https://openalex.org/W1501637923","https://openalex.org/W1528666160","https://openalex.org/W4416505941","https://openalex.org/W2916742098","https://openalex.org/W2282193458","https://openalex.org/W7222797590","https://openalex.org/W4407091482","https://openalex.org/W3162445421","https://openalex.org/W2079536072"],"abstract_inverted_index":{"When":[0],"simulating":[1],"multiscale":[2],"stochastic":[3],"differential":[4],"equations":[5],"(SDEs)":[6],"in":[7],"high-dimensions,":[8],"separation":[9],"of":[10,28,43,124,143,155],"timescales":[11],"and":[12,26,54,62,107,122,134,149],"high-dimensionality":[13],"can":[14,115],"make":[15],"simulations":[16,86],"expensive.":[17],"The":[18,94,111],"computational":[19],"cost":[20],"is":[21,59],"dictated":[22],"by":[23,56],"microscale":[24,53,85,101,161],"properties":[25],"interactions":[27],"many":[29,46],"variables,":[30],"while":[31],"interesting":[32],"behavior":[33],"often":[34],"occurs":[35],"on":[36,152],"the":[37,49,52,100,141,144,153,160],"macroscale":[38,55,70,91,113],"with":[39],"few":[40],"important":[41],"degrees":[42],"freedom.":[44],"For":[45],"problems":[47],"bridging":[48],"gap":[50],"between":[51],"direct":[57],"simulation":[58],"computationally":[60],"infeasible,":[61],"one":[63],"would":[64],"like":[65],"to":[66,87],"learn":[67,88],"a":[68,103,108],"fast":[69,120,145],"simulator.":[71,162],"In":[72],"this":[73],"paper":[74],"we":[75,147],"present":[76],"an":[77],"unsupervised":[78],"learning":[79,95],"algorithm":[80,96],"that":[81],"uses":[82],"short":[83,156],"parallelizable":[84],"provably":[89],"accurate":[90],"SDE":[92],"models.":[93],"takes":[97],"as":[98,136,138],"input:":[99],"simulator,":[102],"local":[104],"distance":[105],"function,":[106],"homogenization":[109],"scale.":[110],"learned":[112],"model":[114],"then":[116],"be":[117],"used":[118],"for":[119],"computation":[121],"storage":[123],"long":[125],"simulations.":[126],"I":[127],"will":[128],"discuss":[129],"various":[130],"examples,":[131],"both":[132],"low-":[133],"high-dimensional,":[135],"well":[137],"results":[139],"about":[140],"accuracy":[142],"simulators":[146],"construct,":[148],"its":[150],"dependency":[151],"number":[154],"paths":[157],"requested":[158],"from":[159]},"counts_by_year":[],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2016-06-24T00:00:00"}
