{"id":"https://openalex.org/W7160627958","doi":"https://doi.org/10.48550/arxiv.2605.05606","title":"Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows","display_name":"Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows","publication_year":2026,"publication_date":"2026-05-07","ids":{"openalex":"https://openalex.org/W7160627958","doi":"https://doi.org/10.48550/arxiv.2605.05606"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05606","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05606","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.2605.05606","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135711814","display_name":"Yu Wang","orcid":"https://orcid.org/0009-0003-5941-7070"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019127650","display_name":"Arnab Ganguly","orcid":"https://orcid.org/0000-0003-3331-0913"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ganguly, Arnab","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":0.8090000152587891,"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":0.8090000152587891,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.05779999867081642,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.047200001776218414,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6383000016212463},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5070000290870667},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4359999895095825},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4162999987602234},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.4077000021934509},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4050000011920929},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.39590001106262207},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.38429999351501465}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6383000016212463},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5070000290870667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4652999937534332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45159998536109924},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.4077000021934509},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39309999346733093},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.38429999351501465},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3564999997615814},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.349700003862381},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C65660741","wikidata":"https://www.wikidata.org/wiki/Q3952743","display_name":"Score","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05606","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05606","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.2605.05606","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05606","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":[{"id":"https://metadata.un.org/sdg/1","display_name":"No poverty","score":0.6132385730743408}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Stochastic":[0],"differential":[1],"equations":[2],"(SDEs)":[3],"provide":[4],"a":[5,57,78,81,123,132,143,167,185,208],"flexible":[6],"framework":[7],"for":[8,40,146,157],"modeling":[9],"temporal":[10],"dynamics":[11,114],"in":[12,67],"partially":[13],"observed":[14],"systems.":[15],"A":[16],"central":[17],"task":[18],"is":[19,176],"to":[20,100,166,178,217],"calibrate":[21],"such":[22],"models":[23],"from":[24,33,194],"data,":[25],"which":[26],"requires":[27],"inferring":[28],"latent":[29],"trajectories":[30],"and":[31,49,106,161,204],"parameters":[32,191],"sparse,":[34],"noisy":[35],"observations.":[36],"Classical":[37],"smoothing":[38,160,181],"methods":[39],"this":[41,53,93],"problem":[42],"are":[43],"often":[44],"limited":[45],"by":[46,184],"path":[47],"degeneracy":[48],"poor":[50],"scalability.":[51],"In":[52],"work,":[54],"we":[55],"developed":[56],"novel":[58],"method":[59],"based":[60],"on":[61,199],"characterization":[62],"of":[63,69,77],"the":[64,75,103,107,127,148,172,180,189,195],"posterior":[65,124,137],"SDE":[66,125,149,190],"terms":[68],"conditional":[70,94,174],"backward-in-time":[71],"score":[72,95,121,175],"defined":[73],"as":[74],"gradient":[76],"function":[79],"solving":[80],"Kolmogorov":[82],"backward":[83],"equation":[84],"with":[85,115,126,207],"multiplicative":[86],"updates":[87],"at":[88],"observation":[89],"times.":[90],"We":[91,140],"learn":[92],"using":[96,192],"neural":[97,173],"networks":[98],"trained":[99],"satisfy":[101],"both":[102],"governing":[104],"PDE":[105],"observation-induced":[108],"jump":[109],"conditions,":[110],"thereby":[111],"integrating":[112],"continuous-time":[113],"discrete":[116],"Bayesian":[117],"updates.":[118],"The":[119],"resulting":[120],"induces":[122],"same":[128],"diffusion":[129],"coefficient":[130],"but":[131],"modified":[133],"drift,":[134],"enabling":[135],"efficient":[136],"trajectory":[138],"sampling.":[139],"further":[141],"derive":[142],"likelihood-based":[144],"objective":[145],"learning":[147],"parameters,":[150],"yielding":[151],"an":[152],"evidence":[153],"lower":[154],"bound":[155],"(ELBO)":[156],"joint":[158],"state":[159],"parameter":[162],"estimation.":[163],"This":[164],"leads":[165],"variational":[168],"EM-style":[169],"procedure,":[170],"where":[171],"optimized":[177],"approximate":[179],"distribution,":[182],"followed":[183],"maximization":[186],"step":[187],"over":[188],"samples":[193],"induced":[196],"posterior.":[197],"Experiments":[198],"nonlinear":[200],"systems":[201],"demonstrate":[202],"accurate":[203],"stable":[205],"inference":[206],"very":[209],"few":[210],"observations":[211],"demonstrating":[212],"significant":[213],"improved":[214],"scalability":[215],"compared":[216],"classical":[218],"MCMC":[219],"methods.":[220]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-09T00:00:00"}