{"id":"https://openalex.org/W7204873628","doi":"https://doi.org/10.48550/arxiv.2608.28869","title":"A priori Assessment of Tensor-Network Encoding for Isotropic Turbulent Flows","display_name":"A priori Assessment of Tensor-Network Encoding for Isotropic Turbulent Flows","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204873628","doi":"https://doi.org/10.48550/arxiv.2608.28869"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28869","pdf_url":"https://arxiv.org/pdf/2608.28869","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/2608.28869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148895066","display_name":"Massen Esmaeili","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Esmaeili, Massen","raw_affiliation_strings":["Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114112589","display_name":"Hirad Alipanah","orcid":"https://orcid.org/0009-0008-3279-2205","observed_orcids":["https://orcid.org/0009-0008-3279-2205"]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alipanah, Hirad","raw_affiliation_strings":["Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120844355","display_name":"Robert Pinkston","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pinkston, Robert","raw_affiliation_strings":["Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078398236","display_name":"Peyman Givi","orcid":"https://orcid.org/0000-0002-9557-5768","observed_orcids":["https://orcid.org/0000-0002-9557-5768"]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Givi, Peyman","raw_affiliation_strings":["Chemical and Petroleum Engineering , University of Pittsburgh , Pittsburgh , PA , USA","Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chemical and Petroleum Engineering , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045656065","display_name":"Daniel Livescu","orcid":"https://orcid.org/0000-0003-2367-1547","observed_orcids":["https://orcid.org/0000-0003-2367-1547"]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Livescu, Daniel","raw_affiliation_strings":["Los Alamos National Laboratory , Los Alamos , NM , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Laboratory , Los Alamos , NM , USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024577147","display_name":"Andrew J. Daley","orcid":"https://orcid.org/0000-0001-9005-7761","observed_orcids":["https://orcid.org/0000-0001-9005-7761"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Daley, Andrew J.","raw_affiliation_strings":["Clarendon Laboratory , University of Oxford , Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clarendon Laboratory , University of Oxford , Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061103540","display_name":"Dieter Jaksch","orcid":"https://orcid.org/0000-0002-9704-3941","observed_orcids":["https://orcid.org/0000-0002-9704-3941"]},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Jaksch, Dieter","raw_affiliation_strings":["Clarendon Laboratory , University of Oxford , Oxford , UK","Institute for Quantum Physics , University of Hamburg , Hamburg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clarendon Laboratory , University of Oxford , Oxford , UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Institute for Quantum Physics , University of Hamburg , Hamburg , Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043433729","display_name":"Juan Jos\u00e9 Mendoza-Arenas","orcid":"https://orcid.org/0000-0002-2214-334X","observed_orcids":["https://orcid.org/0000-0002-2214-334X"]},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mendoza-Arenas, Juan Jos\u00e9","raw_affiliation_strings":["Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mechanical Engineering and Materials Science , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"Physics and Astronomy , University of Pittsburgh , Pittsburgh , PA , USA","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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":0.9746000170707703,"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":0.9746000170707703,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.014999999664723873,"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/T12303","display_name":"Tensor decomposition and applications","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/tensor-networks","display_name":"tensor networks","score":0.949999988079071},{"id":"https://openalex.org/keywords/matrix-product-states","display_name":"matrix product states","score":0.9570000171661377},{"id":"https://openalex.org/keywords/isotropic-turbulence","display_name":"isotropic turbulence","score":0.9340000152587891},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.9829999804496765},{"id":"https://openalex.org/keywords/data-compression","display_name":"data compression","score":0.6629999876022339},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"singular value decomposition","score":0.7559999823570251},{"id":"https://openalex.org/keywords/velocity-field-reconstruction","display_name":"velocity field reconstruction","score":0.6620000004768372},{"id":"https://openalex.org/keywords/scalar-transport","display_name":"scalar transport","score":0.6740000247955322},{"id":"https://openalex.org/keywords/energy-dissipation","display_name":"energy dissipation","score":0.5040000081062317},{"id":"https://openalex.org/keywords/structure-functions","display_name":"structure functions","score":0.8939999938011169},{"id":"https://openalex.org/keywords/velocity-gradient","display_name":"velocity gradient","score":0.7649999856948853}],"concepts":[{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.8440999984741211},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6266999840736389},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.5770000219345093},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5716999769210815},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5404999852180481},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C18533594","wikidata":"https://www.wikidata.org/wiki/Q1227572","display_name":"Direct numerical simulation","level":4,"score":0.4830999970436096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4803999960422516},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.4302999973297119},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3815000057220459},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3677999973297119},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.3582000136375427},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3160000145435333},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30090001225471497},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C2779251355","wikidata":"https://www.wikidata.org/wiki/Q1626189","display_name":"Homogeneous isotropic turbulence","level":5,"score":0.2957000136375427},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2630999982357025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2603999972343445},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28869","pdf_url":"https://arxiv.org/pdf/2608.28869","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.2608.28869","doi":"https://doi.org/10.48550/arxiv.2608.28869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28869","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28869","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28869","pdf_url":"https://arxiv.org/pdf/2608.28869","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204873628.pdf","grobid_xml":"https://content.openalex.org/works/W7204873628.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1570334424","https://openalex.org/W4415343812","https://openalex.org/W4415346154","https://openalex.org/W4416283204","https://openalex.org/W4417095928","https://openalex.org/W4417460362","https://openalex.org/W7131641822","https://openalex.org/W7154985432","https://openalex.org/W7203664824"],"related_works":["https://openalex.org/W7116322815","https://openalex.org/W4417095928","https://openalex.org/W7162990877","https://openalex.org/W4406947850","https://openalex.org/W4389477322","https://openalex.org/W7172398442","https://openalex.org/W2750627203","https://openalex.org/W2946775609","https://openalex.org/W7128034513","https://openalex.org/W4406956380"],"abstract_inverted_index":{"Tensor":[0],"networks":[1],"(TNs),":[2],"originally":[3],"developed":[4],"for":[5,14,246],"simulating":[6],"many-body":[7],"quantum":[8],"systems,":[9],"provide":[10],"a":[11,56,86,91,102],"systematic":[12],"framework":[13,59],"approximating":[15],"high-dimensional":[16],"fields.":[17],"This":[18],"is":[19,52,96,119,131,147],"achieved":[20],"by":[21],"factorizing":[22],"the":[23,34,42,46,77,123,127,139,144,156,169,174,178,207,212,223,235,242],"field":[24,38,79,95,130,176],"into":[25],"interconnected":[26],"tensors":[27],"with":[28],"small":[29,111],"bond":[30],"dimensions,":[31],"thereby":[32],"restricting":[33],"correlations":[35],"captured":[36],"across":[37],"bipartitions.":[39],"Belonging":[40],"to":[41,60,122,150,154],"family":[43],"of":[44,64,80,104,138,143,168,188,234,244,250,258],"TNs,":[45],"matrix":[47],"product":[48],"state":[49],"(MPS)":[50],"ansatz":[51],"utilized":[53],"here":[54],"as":[55,98],"reduced-order":[57,248],"modeling":[58],"construct":[61],"truncated":[62,117],"representations":[63],"isotropic":[65],"turbulent":[66,252],"flow":[67],"data.":[68],"Two":[69],"direct":[70],"numerical":[71],"simulation":[72],"(DNS)":[73],"datasets":[74,253],"are":[75,114,200,215],"considered:":[76],"hydrodynamic":[78],"an":[81,99],"incompressible":[82],"three-dimensional":[83],"flow,":[84],"and":[85,126,190,197,211,226,254],"conserved":[87],"Fickian":[88],"scalar":[89,175,213,228],"in":[90,109,152,261],"similar":[92],"flow.":[93],"Each":[94],"encoded":[97],"MPS":[100,245],"through":[101],"sequence":[103],"singular":[105,112],"value":[106],"decompositions":[107],"(SVDs)":[108],"which":[110],"values":[113],"discarded.":[115],"The":[116],"representation":[118],"contracted":[120],"back":[121],"full":[124],"grid,":[125],"resulting":[128],"reconstructed":[129],"compared":[132],"against":[133],"DNS.":[134],"An":[135],"interleaved":[136],"ordering":[137],"spatial":[140],"tensor":[141],"indices":[142],"transport":[145],"variables":[146],"applied":[148],"prior":[149],"decomposition":[151],"order":[153],"localize":[155],"dominant":[157],"inter-tensor":[158],"correlations.":[159],"Velocity":[160],"reconstructions":[161],"achieve":[162],"$99.8\\%$":[163],"fidelity":[164,180],"using":[165],"only":[166],"$5\\%$":[167],"original":[170],"DNS":[171,236],"memory,":[172],"while":[173,222],"reaches":[177],"same":[179],"at":[181],"$15\\%$":[182],"memory":[183],"usage.":[184],"A":[185],"wide":[186],"range":[187],"lower-":[189],"higher-order":[191],"statistics,":[192],"including":[193],"velocity":[194],"gradients,":[195],"dissipation,":[196],"structure":[198],"functions,":[199],"systematically":[201],"examined.":[202],"At":[203],"these":[204],"compression":[205],"levels,":[206],"total":[208],"kinetic":[209],"energy":[210,214],"both":[216],"recovered":[217],"within":[218,231],"$0.2\\%$":[219],"relative":[220],"error,":[221],"mean":[224,227],"dissipation":[225,229],"remain":[230],"approximately":[232],"$10\\%$":[233],"generated":[237],"values.":[238],"These":[239],"findings":[240],"support":[241],"suitability":[243],"scalable":[247],"analysis":[249],"complex":[251],"motivate":[255],"further":[256],"exploration":[257],"TN-based":[259],"methods":[260],"computational":[262],"turbulence.":[263]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}