{"id":"https://openalex.org/W7213403445","doi":"https://doi.org/10.48550/arxiv.2609.17323","title":"A derivative-free framework for capturing macroscopic behavior of incompressible turbulent flows","display_name":"A derivative-free framework for capturing macroscopic behavior of incompressible turbulent flows","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213403445","doi":"https://doi.org/10.48550/arxiv.2609.17323"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17323","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17323","pdf_url":"https://arxiv.org/pdf/2609.17323","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17323","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151882133","display_name":"Jihun Han","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Han, Jihun","raw_affiliation_strings":["Department of Mathematics and Statistics , University at Albany -State University of New York , Albany , NY 12222"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , University at Albany -State University of New York , Albany , NY 12222","institution_ids":["https://openalex.org/I392282"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151905280","display_name":"Yoonsang Lee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lee, Yoonsang","raw_affiliation_strings":["Department of Mathematics , Dartmouth College , Hanover , NH 03755"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Dartmouth College , Hanover , NH 03755","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9984999895095825,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/incompressible-turbulence","display_name":"incompressible turbulence","score":0.7559999823570251},{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.9020000100135803},{"id":"https://openalex.org/keywords/sampling-noise","display_name":"sampling noise","score":0.7089999914169312},{"id":"https://openalex.org/keywords/energy-spectrum","display_name":"energy spectrum","score":0.8669999837875366},{"id":"https://openalex.org/keywords/two-dimensional-turbulence","display_name":"two-dimensional turbulence","score":0.6639999747276306}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6714000105857849},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5741999745368958},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4672999978065491},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4542999863624573},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4487000107765198},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39750000834465027},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3855000138282776},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28760001063346863},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C18533594","wikidata":"https://www.wikidata.org/wiki/Q1227572","display_name":"Direct numerical simulation","level":4,"score":0.28630000352859497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2833000123500824},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2782999873161316},{"id":"https://openalex.org/C1633027","wikidata":"https://www.wikidata.org/wiki/Q815820","display_name":"Computational fluid dynamics","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2700999975204468},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17323","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17323","pdf_url":"https://arxiv.org/pdf/2609.17323","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":"doi:10.48550/arxiv.2609.17323","doi":"https://doi.org/10.48550/arxiv.2609.17323","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17323","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:2609.17323","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17323","pdf_url":"https://arxiv.org/pdf/2609.17323","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":[{"id":"https://openalex.org/G1922485206","display_name":null,"funder_award_id":"#N00014-20-1-2595","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4174771966","display_name":null,"funder_award_id":"N00014\u201020\u20101\u20102595","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G7428862530","display_name":null,"funder_award_id":"N00014-20-1-2595","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8006577219","display_name":null,"funder_award_id":"N00014-20","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"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/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213403445.pdf","grobid_xml":"https://content.openalex.org/works/W7213403445.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2734960119","https://openalex.org/W4285098939","https://openalex.org/W6948167328","https://openalex.org/W7163889622","https://openalex.org/W7151901436","https://openalex.org/W4298000212","https://openalex.org/W3088681382","https://openalex.org/W2277354692","https://openalex.org/W4413861280","https://openalex.org/W3092919479"],"abstract_inverted_index":{"The":[0,47],"derivative-free":[1],"loss":[2],"method":[3,107,141],"(DFLM)":[4],"is":[5,162],"a":[6,109,124,168],"mesh-free":[7],"neural":[8],"network":[9],"approach":[10],"for":[11,52,171],"solving":[12],"partial":[13],"differential":[14],"equations":[15],"by":[16],"simulating":[17],"stochastic":[18],"walkers":[19,48,65],"rather":[20],"than":[21,154],"computing":[22],"derivatives":[23],"directly.":[24],"Although":[25],"DFLM":[26],"has":[27],"previously":[28],"been":[29],"applied":[30],"to":[31,37,67],"the":[32,53,59,64,69,74,86,105,139,143,155],"Navier--Stokes":[33],"equations,":[34],"extending":[35],"it":[36],"turbulent":[38,136,172],"flows":[39],"reveals":[40],"two":[41,135],"limitations":[42,80],"of":[43,58,85,114,147],"its":[44],"simplest":[45],"implementation.":[46],"do":[49],"not":[50],"account":[51],"swirling,":[54],"directionally":[55],"stretching":[56,93,161],"motion":[57,89],"flow,":[60],"and":[61,94,131],"randomly":[62],"sampling":[63,97],"used":[66],"evaluate":[68],"target":[70],"introduces":[71],"noise":[72],"into":[73],"learned":[75],"solution.":[76],"We":[77,103],"address":[78],"both":[79],"with":[81],"an":[82],"analytic":[83],"approximation":[84],"walkers'":[87],"local":[88],"that":[90],"captures":[91],"directional":[92,160],"eliminates":[95],"this":[96],"noise,":[98],"while":[99],"remaining":[100],"computationally":[101],"efficient.":[102],"study":[104],"resulting":[106],"as":[108,167],"non-intrusive":[110],"multiscale":[111,169],"solver":[112,170],"capable":[113],"learning":[115],"macroscopic":[116,144],"flow":[117],"behavior":[118],"without":[119],"resolving":[120],"every":[121],"scale":[122],"on":[123],"fine":[125],"grid":[126],"or":[127],"explicitly":[128],"coupling":[129],"coarse-":[130],"fine-scale":[132],"models.":[133],"For":[134],"two-dimensional":[137],"flows,":[138],"proposed":[140],"reproduces":[142],"energy":[145],"spectrum":[146],"fully":[148],"resolved":[149],"reference":[150],"simulations":[151],"more":[152],"accurately":[153],"standard":[156],"method,":[157],"particularly":[158],"where":[159],"strongest,":[163],"confirming":[164],"DFLM's":[165],"efficacy":[166],"fluid":[173],"systems.":[174]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-17T00:00:00"}