{"id":"https://openalex.org/W7136868920","doi":"https://doi.org/10.48550/arxiv.2603.12635","title":"Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems","display_name":"Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems","publication_year":2026,"publication_date":"2026-03-13","ids":{"openalex":"https://openalex.org/W7136868920","doi":"https://doi.org/10.48550/arxiv.2603.12635"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.12635","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12635","pdf_url":null,"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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.12635","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101393726","display_name":"Dibyajyoti Chakraborty","orcid":"https://orcid.org/0000-0001-9844-1020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chakraborty, Dibyajyoti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129439500","display_name":"Hojin Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Hojin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129549630","display_name":"Romit Maulik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maulik, Romit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.8015999794006348,"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":0.8015999794006348,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.05420000106096268,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.01720000058412552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.4982999861240387},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48159998655319214},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4309999942779541},{"id":"https://openalex.org/keywords/sensor-fusion","display_name":"Sensor fusion","score":0.42250001430511475},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.41850000619888306},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40619999170303345},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4032000005245209},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.39910000562667847},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.362199991941452}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5843999981880188},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.4982999861240387},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48159998655319214},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C33954974","wikidata":"https://www.wikidata.org/wiki/Q486494","display_name":"Sensor fusion","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40619999170303345},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4032000005245209},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3197000026702881},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.29670000076293945},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2825999855995178},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2777000069618225},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.27469998598098755},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.259799987077713},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.12635","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12635","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.12635","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12635","pdf_url":null,"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":"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"High-fidelity":[0],"numerical":[1],"simulations":[2],"of":[3,16,46,142,162],"chaotic,":[4],"high":[5,196],"dimensional":[6,197],"nonlinear":[7],"dynamical":[8],"systems":[9,25],"are":[10,26,33,153],"computationally":[11],"expensive,":[12],"necessitating":[13],"the":[14,42,140,143,163],"development":[15],"efficient":[17],"surrogate":[18,21,53,164],"models.":[19],"Most":[20],"models":[22,37],"for":[23,28,127,177,195],"such":[24],"deterministic,":[27],"example":[29],"when":[30],"neural":[31],"operators":[32],"involved.":[34],"However,":[35],"deterministic":[36],"often":[38],"fail":[39],"to":[40,69,90],"capture":[41],"intrinsic":[43],"distributional":[44],"uncertainty":[45,132],"chaotic":[47,198],"systems.":[48,199],"This":[49],"work":[50],"presents":[51],"a":[52,62,79,101,118,178,181],"modeling":[54,115],"formulation":[55],"that":[56,84,121],"leverages":[57],"generative":[58],"machine":[59],"learning,":[60],"where":[61],"deep":[63],"learning":[64],"diffusion":[65,82,107,156],"model":[66],"is":[67],"used":[68],"probabilistically":[70],"forecast":[71],"turbulent":[72],"flows":[73],"over":[74,180],"long":[75],"horizons.":[76],"We":[77,166],"introduce":[78],"multi-step":[80],"autoregressive":[81],"objective":[83],"significantly":[85],"enhances":[86],"long-rollout":[87],"stability":[88],"compared":[89],"standard":[91],"single-step":[92],"training.":[93],"To":[94],"handle":[95],"complex,":[96],"unstructured":[97],"geometries,":[98],"we":[99],"utilize":[100],"multi-scale":[102],"graph":[103],"transformer":[104],"architecture":[105],"incorporating":[106],"preconditioning":[108],"and":[109,173,176,192],"voxel-grid":[110],"pooling.":[111],"More":[112],"importantly,":[113],"our":[114,168],"framework":[116],"provides":[117],"unified":[119],"platform":[120],"also":[122],"predicts":[123],"spatiotemporally":[124],"important":[125],"locations":[126,152],"sensor":[128,151,190],"placement,":[129,191],"either":[130],"via":[131],"estimates":[133],"or":[134],"through":[135],"an":[136],"error-estimation":[137],"module.":[138],"Finally,":[139],"observations":[141],"ground":[144],"truth":[145],"state":[146],"at":[147],"these":[148],"dynamically":[149],"varying":[150],"assimilated":[154],"using":[155],"posterior":[157],"sampling":[158],"requiring":[159],"no":[160],"retraining":[161],"model.":[165],"present":[167],"methodology":[169],"on":[170],"two-dimensional":[171],"homogeneous":[172],"isotropic":[174],"turbulence":[175],"flow":[179],"backwards-facing":[182],"step,":[183],"demonstrating":[184],"its":[185],"utility":[186],"in":[187],"forecasting,":[188],"adaptive":[189],"data":[193],"assimilation":[194]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-17T00:00:00"}
