{"id":"https://openalex.org/W7134838736","doi":"https://doi.org/10.48550/arxiv.2603.08465","title":"MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries","display_name":"MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134838736","doi":"https://doi.org/10.48550/arxiv.2603.08465"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.08465","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08465","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,"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.2603.08465","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128685474","display_name":"Weizheng Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Weizheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030874500","display_name":"Xunjie Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Xunjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128688783","display_name":"Hao Pan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pan, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005199524","display_name":"Xiaowei Duan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Duan, Xiaowei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128641265","display_name":"Bingteng Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Bingteng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128678169","display_name":"Qiang Du","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Du, Qiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Lu, Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Lin","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":0.899399995803833,"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":0.899399995803833,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.017100000753998756,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.01080000028014183,"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/conservation-law","display_name":"Conservation law","score":0.6399999856948853},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5914000272750854},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5570999979972839},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5486999750137329},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5479999780654907},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.4794999957084656},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.4731000065803528},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.46950000524520874},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.46219998598098755},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.44929999113082886}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6399999856948853},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5914000272750854},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5570999979972839},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5486999750137329},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5479999780654907},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4593999981880188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4584999978542328},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4300999939441681},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4230000078678131},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4083000123500824},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39959999918937683},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.3718999922275543},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32269999384880066},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C186766456","wikidata":"https://www.wikidata.org/wiki/Q612457","display_name":"Flow control (data)","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.272599995136261},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C1633027","wikidata":"https://www.wikidata.org/wiki/Q815820","display_name":"Computational fluid dynamics","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.25220000743865967},{"id":"https://openalex.org/C180925781","wikidata":"https://www.wikidata.org/wiki/Q514096","display_name":"Open-channel flow","level":3,"score":0.25189998745918274},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.08465","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08465","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,"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.2603.08465","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08465","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,"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":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6359093189239502}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"While":[0],"Physics-Informed":[1],"Neural":[2],"Networks":[3],"(PINNs)":[4],"offer":[5],"a":[6,90,112],"mesh-free":[7],"approach":[8],"to":[9,38,136],"solving":[10],"fluid-flow":[11],"PDEs,":[12],"standard":[13],"point-wise":[14,35],"residual":[15],"minimization":[16],"suffers":[17],"from":[18],"convergence":[19],"pathologies":[20],"in":[21,123],"topologically":[22],"complex":[23],"domains":[24],"like":[25],"Triply":[26],"Periodic":[27],"Minimal":[28],"Surfaces":[29],"(TPMS).":[30],"The":[31],"locality":[32],"bias":[33],"of":[34],"constraints":[36,65],"fails":[37],"propagate":[39],"global":[40],"information":[41],"through":[42],"tortuous":[43],"channels,":[44],"causing":[45],"unstable":[46],"gradients":[47],"and":[48,78,106,138],"conservation":[49,68,80],"violations.":[50],"To":[51],"address":[52],"this,":[53],"we":[54],"propose":[55],"the":[56],"Multi-scale":[57],"Weak-form":[58],"PINN":[59],"(MUSA-PINN),":[60],"which":[61],"reformulates":[62],"Navier-Stokes":[63],"equation":[64],"as":[66],"integral":[67],"laws":[69],"over":[70],"hierarchical":[71],"spherical":[72],"control":[73,85],"volumes.":[74],"We":[75],"enforce":[76],"continuity":[77],"momentum":[79],"via":[81],"flux-balance":[82],"residuals":[83],"on":[84,119],"surfaces.":[86],"Our":[87],"method":[88],"utilizes":[89],"three-scale":[91],"subdomain":[92],"strategy-comprising":[93],"large":[94],"volumes":[95,101,108],"for":[96,109],"long-range":[97],"coupling,":[98],"skeleton-aware":[99],"meso-scale":[100],"aligned":[102],"with":[103],"transport":[104],"pathways,":[105],"small":[107],"local":[110],"refinement-alongside":[111],"two-stage":[113],"training":[114],"schedule":[115],"prioritizing":[116],"continuity.":[117],"Experiments":[118],"steady":[120],"incompressible":[121],"flow":[122],"TPMS":[124],"geometries":[125],"show":[126],"MUSA-PINN":[127],"outperforms":[128],"state-of-the-art":[129],"baselines,":[130],"reducing":[131],"relative":[132],"errors":[133],"by":[134],"up":[135],"93%":[137],"preserving":[139],"mass":[140],"conservation.":[141]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-11T00:00:00"}
