{"id":"https://openalex.org/W7127338582","doi":"https://doi.org/10.48550/arxiv.2602.01941","title":"FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates","display_name":"FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127338582","doi":"https://doi.org/10.48550/arxiv.2602.01941"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.01941","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","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/A5108915573","display_name":"Zishuo Lan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lan, Zishuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124882024","display_name":"Junjie Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Junjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124924760","display_name":"Lei Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124950483","display_name":"Jincheng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jincheng","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14173514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.638700008392334,"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":0.638700008392334,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.16519999504089355,"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":0.07039999961853027,"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/pointwise","display_name":"Pointwise","score":0.7376999855041504},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6784999966621399},{"id":"https://openalex.org/keywords/spinodal","display_name":"Spinodal","score":0.5109000205993652},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.4666000008583069},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44449999928474426},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.414900004863739},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.3440999984741211},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.3147999942302704}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7376999855041504},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6784999966621399},{"id":"https://openalex.org/C85272257","wikidata":"https://www.wikidata.org/wiki/Q907839","display_name":"Spinodal","level":3,"score":0.5109000205993652},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.4666000008583069},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4262000024318695},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41620001196861267},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.414900004863739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4147000014781952},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4115000069141388},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2964000105857849},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.26089999079704285},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C177606310","wikidata":"https://www.wikidata.org/wiki/Q5674297","display_name":"Adaptability","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.01941","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.01941","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.01941","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.01941","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6291549801826477}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Autoregressive":[0],"learning":[1],"of":[2,38],"time-stepping":[3],"operators":[4],"provides":[5],"an":[6],"effective":[7],"approach":[8],"to":[9,147],"data-driven":[10],"partial":[11],"differential":[12],"equation":[13],"(PDE)":[14],"simulation,":[15],"yet":[16],"for":[17],"conservation":[18,30,92],"laws,":[19],"they":[20],"face":[21],"a":[22,78],"fundamental":[23],"challenge:":[24],"learned":[25],"updates":[26],"may":[27],"violate":[28],"global":[29],"over":[31,81,175],"long":[32],"rollouts.":[33],"For":[34],"the":[35,41,69,82,145],"important":[36],"subclass":[37],"mass-conservation-type":[39],"equations,":[40],"problem":[42],"is":[43,184],"compounded":[44],"by":[45,93],"inherent":[46],"physical":[47],"bounds":[48],"(e.g.,":[49],"nonnegativity":[50],"or":[51,108],"concentrations":[52],"in":[53],"[0,1])":[54],"whose":[55],"violation":[56],"further":[57],"destabilizes":[58],"predictions.":[59],"We":[60],"introduce":[61],"FluxNet,":[62],"which":[63],"learns":[64],"cumulative":[65],"transport":[66,97,133],"amounts":[67],"representing":[68],"total":[70],"conserved":[71],"quantity":[72],"redistributed":[73],"between":[74],"each":[75],"cell":[76],"and":[77,101,122,172],"configurable":[79,132],"neighborhood":[80],"full":[83,139],"surrogate":[84],"interval.":[85],"A":[86],"conservative":[87],"update":[88],"guarantees":[89],"exact":[90,165],"discrete":[91],"construction;":[94],"modular":[95],"capacity-constrained":[96],"heads":[98],"(L,":[99],"U,":[100],"D)":[102],"enforce":[103],"lower":[104],"bounds,":[105,107],"upper":[106],"near-zero":[109],"dual-bound":[110],"violations":[111],"through":[112],"architectural":[113],"design.":[114],"Unlike":[115],"flux-rate":[116,176],"surrogates":[117,177],"that":[118],"require":[119],"temporal":[120,180],"integration":[121],"thus":[123],"inherit":[124],"CFL":[125],"constraints,":[126],"FluxNet":[127],"involves":[128],"no":[129],"such":[130],"integration;":[131],"neighborhoods":[134],"enable":[135],"large-timestep":[136],"prediction":[137],"at":[138,178],"spatial":[140],"resolution.":[141],"Ghost":[142],"cells":[143],"extend":[144],"framework":[146],"non-periodic":[148],"boundaries.":[149],"Experiments":[150],"on":[151],"four":[152],"benchmarks":[153],"(1D":[154],"convection--diffusion,":[155],"2D":[156,162],"shallow":[157],"water,":[158],"1D":[159],"traffic":[160],"flow,":[161],"Cahn--Hilliard)":[163],"demonstrate":[164],"conservation,":[166],"structural":[167],"bound":[168],"preservation,":[169],"architecture":[170],"modularity,":[171],"superior":[173],"stability":[174],"large":[179],"strides.":[181],"The":[182],"code":[183],"publicly":[185],"available":[186],"at:":[187],"https://github.com/Lan-zs/FluxNet.":[188]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-04T00:00:00"}
