{"id":"https://openalex.org/W7125608365","doi":"https://doi.org/10.1016/j.neunet.2026.108641","title":"Benchmarking autoregressive conditional diffusion models for turbulent flow simulation","display_name":"Benchmarking autoregressive conditional diffusion models for turbulent flow simulation","publication_year":2026,"publication_date":"2026-01-24","ids":{"openalex":"https://openalex.org/W7125608365","doi":"https://doi.org/10.1016/j.neunet.2026.108641","pmid":"https://pubmed.ncbi.nlm.nih.gov/41662807"},"language":"en","primary_location":{"id":"doi:10.1016/j.neunet.2026.108641","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neunet.2026.108641","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.neunet.2026.108641","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123762366","display_name":"Georg Kohl","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Georg Kohl","raw_affiliation_strings":["Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: georg.kohl@tum.de"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: georg.kohl@tum.de","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123750311","display_name":"Li-Wei Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Li-Wei Chen","raw_affiliation_strings":["Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: jilinchl@163.com"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: jilinchl@163.com","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123187512","display_name":"Nils Thuerey","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nils Thuerey","raw_affiliation_strings":["Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: nils.thuerey@tum.de"],"affiliations":[{"raw_affiliation_string":"Technical University of Munich, Boltzmannstra\u00dfe 3, Garching, 85748, Germany. Electronic address: nils.thuerey@tum.de","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5123762366"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":3350,"currency":"USD","value_usd":3350},"apc_paid":{"value":3350,"currency":"USD","value_usd":3350},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23287671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"199","issue":null,"first_page":"108641","last_page":"108641"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9625999927520752,"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":0.9625999927520752,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.01720000058412552,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.002199999988079071,"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/benchmark","display_name":"Benchmark (surveying)","score":0.7124999761581421},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.6068000197410583},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5925999879837036},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5824999809265137},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5013999938964844},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.47780001163482666},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4691999852657318},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.39309999346733093}],"concepts":[{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7124999761581421},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6758000254631042},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.6068000197410583},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5925999879837036},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5824999809265137},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4691999852657318},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4359000027179718},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.3806000053882599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3725999891757965},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.36970001459121704},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35440000891685486},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C103838597","wikidata":"https://www.wikidata.org/wiki/Q1579556","display_name":"Transonic","level":3,"score":0.32499998807907104},{"id":"https://openalex.org/C1633027","wikidata":"https://www.wikidata.org/wiki/Q815820","display_name":"Computational fluid dynamics","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.301800012588501},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2743000090122223},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2583000063896179},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2572000026702881}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.neunet.2026.108641","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neunet.2026.108641","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},{"id":"pmid:41662807","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41662807","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural networks : the official journal of the International Neural Network Society","raw_type":null}],"best_oa_location":{"id":"doi:10.1016/j.neunet.2026.108641","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.neunet.2026.108641","pdf_url":null,"source":{"id":"https://openalex.org/S123019304","display_name":"Neural Networks","issn_l":"0893-6080","issn":["0893-6080","1879-2782"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W2052824539","https://openalex.org/W2075843680","https://openalex.org/W2097663931","https://openalex.org/W2131908956","https://openalex.org/W2566620089","https://openalex.org/W2777417212","https://openalex.org/W2805869290","https://openalex.org/W2864723431","https://openalex.org/W2891039272","https://openalex.org/W2951392159","https://openalex.org/W2964027982","https://openalex.org/W2965742591","https://openalex.org/W2981620309","https://openalex.org/W2985630280","https://openalex.org/W3082908155","https://openalex.org/W3161200675","https://openalex.org/W3216107495","https://openalex.org/W4245992388","https://openalex.org/W4298000212","https://openalex.org/W4317725853","https://openalex.org/W4318978575","https://openalex.org/W4360618437","https://openalex.org/W4376958741","https://openalex.org/W4377246425","https://openalex.org/W4387195417","https://openalex.org/W4388702043","https://openalex.org/W4398174240"],"related_works":[],"abstract_inverted_index":{"Simulating":[0],"turbulent":[1],"flows":[2],"is":[3],"crucial":[4],"for":[5,33,167,192],"a":[6,30,58],"wide":[7],"range":[8],"of":[9,94,131,156,163,176],"applications,":[10],"and":[11,72,89,105,133],"machine":[12],"learning-based":[13],"solvers":[14,46],"are":[15,57,113,152,190],"gaining":[16],"increasing":[17],"relevance.":[18],"However,":[19],"achieving":[20],"temporal":[21,73,134],"stability":[22],"when":[23],"generalizing":[24],"to":[25,61,80],"longer":[26],"rollout":[27,51],"horizons":[28],"remains":[29],"persistent":[31],"challenge":[32],"learned":[34],"PDE":[35],"solvers.":[36],"In":[37],"this":[38,63],"work,":[39],"we":[40],"analyze":[41],"if":[42],"fully":[43],"data-driven":[44],"fluid":[45],"that":[47,77,117,171,189],"utilize":[48],"an":[49],"autoregressive":[50],"based":[52],"on":[53,138],"conditional":[54],"diffusion":[55,164],"models":[56],"viable":[59],"option":[60],"address":[62],"challenge.":[64],"We":[65,115],"investigate":[66],"accuracy,":[67],"posterior":[68],"sampling,":[69],"spectral":[70],"behavior,":[71],"stability,":[74,135],"while":[75,136],"requiring":[76],"methods":[78,128],"generalize":[79],"flow":[81,96,126,198],"parameters":[82],"beyond":[83],"the":[84,92,160,174,177],"training":[85,147],"regime.":[86],"To":[87],"quantitatively":[88],"qualitatively":[90],"benchmark":[91,182],"performance":[93],"various":[95,196],"prediction":[97,127,199],"approaches,":[98],"three":[99,184],"challenging":[100],"2D":[101],"scenarios":[102],"including":[103],"incompressible":[104],"transonic":[106],"flows,":[107],"as":[108,110],"well":[109],"isotropic":[111],"turbulence":[112],"employed.":[114],"find":[116],"even":[118],"simple":[119],"diffusion-based":[120],"approaches":[121,165],"can":[122],"outperform":[123],"multiple":[124,169],"established":[125,197],"in":[129,154],"terms":[130,155],"accuracy":[132],"being":[137],"par":[139],"with":[140,173],"state-of-the-art":[141],"stabilization":[142],"techniques":[143],"like":[144],"unrolling":[145],"at":[146],"time.":[148],"Such":[149],"traditional":[150],"architectures":[151],"superior":[153],"inference":[157],"speed,":[158],"however,":[159],"probabilistic":[161,193],"nature":[162],"allows":[166],"inferring":[168],"predictions":[170],"align":[172],"statistics":[175],"underlying":[178],"physics.":[179],"Overall,":[180],"our":[181],"contains":[183],"carefully":[185],"chosen":[186],"data":[187],"sets":[188],"suitable":[191],"evaluation":[194],"alongside":[195],"architectures.":[200]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-01-25T00:00:00"}
