{"id":"https://openalex.org/W7131093384","doi":"https://doi.org/10.48550/arxiv.2602.17773","title":"Learning Flow Distributions via Projection-Constrained Diffusion on Manifolds","display_name":"Learning Flow Distributions via Projection-Constrained Diffusion on Manifolds","publication_year":2026,"publication_date":"2026-02-19","ids":{"openalex":"https://openalex.org/W7131093384","doi":"https://doi.org/10.48550/arxiv.2602.17773"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.17773","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119825203","display_name":"Noah Trupin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Trupin, Noah","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106666882","display_name":"Rahul Ghosh","orcid":"https://orcid.org/0000-0001-7644-6568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghosh, Rahul","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126589874","display_name":"Aadi Jangid","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jangid, Aadi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5119825203"],"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.4634000062942505,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.4634000062942505,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.32429999113082886,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.02669999934732914,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/diffusion-map","display_name":"Diffusion map","score":0.5960000157356262},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5794000029563904},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5338000059127808},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.476500004529953},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.46650001406669617},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.46059998869895935},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.43209999799728394},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.42570000886917114}],"concepts":[{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.5960000157356262},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5794000029563904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.534500002861023},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.476500004529953},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.46650001406669617},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.46059998869895935},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4140999913215637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39500001072883606},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38839998841285706},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.34450000524520874},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.302700012922287},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29330000281333923},{"id":"https://openalex.org/C178944513","wikidata":"https://www.wikidata.org/wiki/Q1344391","display_name":"Enstrophy","level":4,"score":0.27459999918937683},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.17773","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.17773","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.17773","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.17773","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6773192286491394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,82],"present":[1],"a":[2,49,58,63,68,78,87,102,156],"generative":[3,159],"modeling":[4,160],"framework":[5],"for":[6,158],"synthesizing":[7],"physically":[8],"feasible":[9],"two-dimensional":[10],"incompressible":[11,113,162],"flows":[12],"under":[13],"arbitrary":[14],"obstacle":[15],"geometries":[16],"and":[17,66,108,121,133,140,147,154,167],"boundary":[18,134],"conditions.":[19],"Whereas":[20],"existing":[21],"diffusion-based":[22],"flow":[23,114,123],"generators":[24],"either":[25],"ignore":[26],"physical":[27,149],"constraints,":[28],"impose":[29],"soft":[30,146],"penalties":[31],"that":[32,73],"do":[33],"not":[34],"guarantee":[35],"feasibility,":[36],"or":[37],"specialize":[38],"to":[39,90,137],"fixed":[40],"geometries,":[41],"our":[42],"approach":[43],"integrates":[44],"three":[45],"complementary":[46],"components:":[47],"(1)":[48],"boundary-conditioned":[50],"diffusion":[51,71,106,152],"model":[52],"operating":[53],"on":[54,94,117],"velocity":[55],"fields;":[56],"(2)":[57],"physics-informed":[59],"training":[60],"objective":[61],"incorporating":[62],"divergence":[64],"penalty;":[65],"(3)":[67],"projection-constrained":[69],"reverse":[70],"process":[72],"enforces":[74],"exact":[75],"incompressibility":[76],"through":[77],"geometry-aware":[79],"Helmholtz-Hodge":[80],"operator.":[81],"derive":[83],"the":[84,95],"method":[85],"as":[86],"discrete":[88],"approximation":[89],"constrained":[91],"Langevin":[92],"sampling":[93],"manifold":[96],"of":[97,161],"divergence-free":[98],"vector":[99],"fields,":[100],"providing":[101],"connection":[103],"between":[104],"modern":[105],"models":[107,153],"geometric":[109],"constraint":[110],"enforcement":[111],"in":[112,164],"spaces.":[115],"Experiments":[116],"analytic":[118],"Navier-Stokes":[119],"data":[120],"obstacle-bounded":[122],"configurations":[124],"demonstrate":[125],"significantly":[126],"improved":[127],"divergence,":[128],"spectral":[129],"accuracy,":[130],"vorticity":[131],"statistics,":[132],"consistency":[135],"relative":[136],"unconstrained,":[138],"projection-only,":[139],"penalty-only":[141],"baselines.":[142],"Our":[143],"formulation":[144],"unifies":[145],"hard":[148],"structure":[150],"within":[151],"provides":[155],"foundation":[157],"fields":[163],"robotics,":[165],"graphics,":[166],"scientific":[168],"computing.":[169]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-24T00:00:00"}