{"id":"https://openalex.org/W7162638390","doi":"https://doi.org/10.48550/arxiv.2605.28291","title":"Dual Variational Neural Network for the $p$-Laplace Problem","display_name":"Dual Variational Neural Network for the $p$-Laplace Problem","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162638390","doi":"https://doi.org/10.48550/arxiv.2605.28291"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.28291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28291","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":null,"license_id":null,"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.2605.28291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091381333","display_name":"Tianhao Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Tianhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137234808","display_name":"Guanglian Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Guanglian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023537612","display_name":"Fengru Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Fengru","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048462943","display_name":"Yifeng Xu","orcid":"https://orcid.org/0009-0006-3216-1310"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Yifeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137216395","display_name":"Zhi Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Zhi","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":0.8511999845504761,"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":0.8511999845504761,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.035999998450279236,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.012199999764561653,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6592000126838684},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5060999989509583},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43810001015663147},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4153999984264374},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4066999852657318},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.40059998631477356},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.3781000077724457},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.37790000438690186}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6592000126838684},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4984000027179718},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4129999876022339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40779998898506165},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4066999852657318},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.40059998631477356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36910000443458557},{"id":"https://openalex.org/C147457402","wikidata":"https://www.wikidata.org/wiki/Q1588205","display_name":"Conservative vector field","level":3,"score":0.3677000105381012},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3564999997615814},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.32269999384880066},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3147999942302704},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3111000061035156},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C2777749129","wikidata":"https://www.wikidata.org/wiki/Q17148469","display_name":"Robust principal component analysis","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.28291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28291","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.28291","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28291","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":null,"license_id":null,"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":{"The":[0,62,130],"reliable":[1],"and":[2,19,70,92,120,163],"accurate":[3],"numerical":[4,39],"approximation":[5],"of":[6,126,149],"the":[7,13,24,54,77,89,101,105,118,127,150,157,170],"$p$-Laplacian":[8],"is":[9,64],"particularly":[10],"challenging":[11,154],"in":[12,37,153],"extreme":[14,158],"regimes":[15],"$p":[16,20,160,164],"\\to":[17,161],"1^{+}$":[18,162],"\\gg":[21,165],"1$,":[22,166],"where":[23],"operator":[25],"becomes":[26],"either":[27],"highly":[28],"singular":[29],"or":[30],"strongly":[31],"degenerate,":[32],"often":[33],"causing":[34],"severe":[35],"instability":[36],"standard":[38],"methods.":[40],"To":[41],"address":[42],"these":[43],"difficulties,":[44],"we":[45,107],"propose":[46],"a":[47,67,84,113],"novel":[48],"deep":[49],"learning":[50,142],"based":[51,65],"framework,":[52],"termed":[53],"dual":[55],"variational":[56],"neural":[57,110,128],"network,":[58],"for":[59,88,100],"$p$-Laplace":[60],"problems.":[61],"approach":[63],"on":[66,133],"mixed":[68],"formulation":[69],"an":[71,93,123],"$L^q$-based":[72],"Helmholtz":[73],"decomposition,":[74,106],"which":[75],"decouples":[76],"original":[78],"problem":[79,87,96],"into":[80],"two":[81,109],"convex":[82],"subproblems:":[83],"linear":[85],"Poisson":[86],"irrotational":[90],"component":[91],"unconstrained":[94],"minimization":[95],"over":[97],"divergence-free":[98],"fields":[99],"solenoidal":[102],"component.":[103],"Following":[104],"employ":[108],"networks":[111],"using":[112],"gradient--curl":[114],"representation":[115],"to":[116],"approximate":[117],"flux,":[119],"further":[121],"establish":[122],"error":[124],"analysis":[125,131],"approximation.":[129],"relies":[132],"fundamental":[134],"vector":[135],"inequalities":[136],"together":[137],"with":[138],"tools":[139],"from":[140],"statistical":[141],"theory.":[143],"Numerical":[144],"experiments":[145],"demonstrate":[146],"robust":[147],"convergence":[148],"proposed":[151],"method":[152],"settings,":[155],"including":[156],"cases":[159],"as":[167,169],"well":[168],"$p(x)$-Laplace":[171],"equation.":[172]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-29T00:00:00"}
