{"id":"https://openalex.org/W7155218651","doi":"https://doi.org/10.48550/arxiv.2604.19601","title":"Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs","display_name":"Quadrature-Enhanced Monte Carlo fPINN Method for High-Dimensional Fractional PDEs","publication_year":2026,"publication_date":"2026-04-21","ids":{"openalex":"https://openalex.org/W7155218651","doi":"https://doi.org/10.48550/arxiv.2604.19601"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.19601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19601","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":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.2604.19601","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134324545","display_name":"Qingkui Ma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Qingkui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134303996","display_name":"Hehu Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Hehu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134361334","display_name":"Xiaobo Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Xiaobo","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":0.8942999839782715,"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":0.8942999839782715,"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/T10514","display_name":"Numerical methods in engineering","score":0.03830000013113022,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0066999997943639755,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6614999771118164},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.5903000235557556},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.546999990940094},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4345000088214874},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.40529999136924744},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.38339999318122864},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.37070000171661377},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.36059999465942383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6972000002861023},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6614999771118164},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.5903000235557556},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.546999990940094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4884999990463257},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4345000088214874},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.40529999136924744},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.38339999318122864},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.37070000171661377},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.36059999465942383},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.329800009727478},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.27880001068115234},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.19601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19601","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":"doi:10.48550/arxiv.2604.19601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19601","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":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":{"Fractional":[0],"PDEs":[1,134],"involving":[2],"the":[3,23,52,71,78,88,103,107,110,138,141],"fractional":[4,53,119,128,133],"Laplacian":[5],"on":[6,127,137],"bounded":[7],"domains":[8],"are":[9],"challenging":[10],"because":[11],"of":[12,51],"hypersingular":[13],"nonlocal":[14],"kernels,":[15],"exterior":[16,62],"Dirichlet":[17],"constraints,":[18],"reduced":[19],"boundary":[20,158],"regularity,":[21],"and":[22,60,83,131,151],"high":[24,28],"computational":[25],"cost":[26],"in":[27,149],"dimensions.":[29],"To":[30],"address":[31],"these":[32],"issues,":[33],"we":[34,66,113],"first":[35],"adopt":[36],"a":[37,47,115],"spatially":[38],"varying":[39],"radius":[40],"with":[41,156],"directional":[42],"distance-to-boundary":[43],"information,":[44],"which":[45],"yields":[46],"geometry-adaptive":[48],"three-part":[49],"decomposition":[50],"Laplacian:":[54],"singular":[55,72],"near-field,":[56],"regular":[57,79],"interior":[58,80],"far-field,":[59],"analytical":[61],"far-field":[63],"contributions.":[64],"Then":[65],"employ":[67],"Gauss-Jacobi":[68],"quadrature":[69,76],"for":[70,77,87,154],"radial":[73,81],"integral,":[74,82],"Gauss":[75],"Monte":[84,117],"Carlo":[85,118],"sampling":[86],"angular":[89],"variables.":[90],"A":[91],"feature-enhanced":[92],"physics-informed":[93,120],"neural":[94,121],"network":[95,122],"trial":[96],"space":[97],"is":[98],"finally":[99],"used":[100],"to":[101],"tackle":[102],"low-regularity":[104],"behavior":[105],"near":[106],"boundary.":[108],"Through":[109],"above":[111],"steps,":[112],"obtain":[114],"quadrature-enhanced":[116],"(QE-MC-fPINN)":[123],"method.":[124],"Numerical":[125],"experiments":[126],"Poisson":[129],"equations":[130],"time-dependent":[132],"show":[135],"that,":[136],"tested":[139],"benchmarks,":[140],"proposed":[142],"method":[143],"outperforms":[144],"two":[145],"representative":[146],"MC-fPINN":[147],"discretizations":[148],"accuracy":[150],"convergence,":[152],"especially":[153],"solutions":[155],"strong":[157],"singularities.":[159]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-23T00:00:00"}
