{"id":"https://openalex.org/W7155514132","doi":"https://doi.org/10.48550/arxiv.2604.21717","title":"Monte Carlo PDE Solvers for Nonlinear Radiative Boundary Conditions","display_name":"Monte Carlo PDE Solvers for Nonlinear Radiative Boundary Conditions","publication_year":2026,"publication_date":"2026-04-22","ids":{"openalex":"https://openalex.org/W7155514132","doi":"https://doi.org/10.48550/arxiv.2604.21717"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.21717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21717","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.21717","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134502962","display_name":"Anchang Bao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bao, Anchang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134508199","display_name":"Enya Shen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Enya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134535729","display_name":"Jianmin Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jianmin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.2953000068664551,"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":0.2953000068664551,"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":0.09380000084638596,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.05510000139474869,"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.7454000115394592},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5910000205039978},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5338000059127808},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.5120000243186951},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.4986000061035156},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4569999873638153},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.43220001459121704},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4320000112056732}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7454000115394592},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5537999868392944},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.5120000243186951},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.4986000061035156},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48080000281333923},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.43220001459121704},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4320000112056732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4092999994754791},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.40860000252723694},{"id":"https://openalex.org/C37669827","wikidata":"https://www.wikidata.org/wiki/Q6904703","display_name":"Monte Carlo molecular modeling","level":4,"score":0.40059998631477356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39570000767707825},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C121683094","wikidata":"https://www.wikidata.org/wiki/Q3554721","display_name":"Control variates","level":5,"score":0.3610999882221222},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3215999901294708},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C89394759","wikidata":"https://www.wikidata.org/wiki/Q192593","display_name":"Thermal radiation","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C122592724","wikidata":"https://www.wikidata.org/wiki/Q3855635","display_name":"Dynamic Monte Carlo method","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C89720835","wikidata":"https://www.wikidata.org/wiki/Q1531701","display_name":"Global illumination","level":3,"score":0.262800008058548}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.21717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21717","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.21717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21717","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":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Monte":[0,62,125],"Carlo":[1,63,126],"PDE":[2,64],"solvers":[3,65],"have":[4],"become":[5],"increasingly":[6],"popular":[7],"for":[8,137],"solving":[9],"heat-related":[10],"partial":[11],"differential":[12],"equations":[13],"in":[14,24,124],"geometry":[15],"processing":[16],"and":[17,35,84,166],"computer":[18],"graphics":[19],"due":[20],"to":[21,66,106],"their":[22],"robustness":[23],"handling":[25],"complex":[26,176],"geometries.":[27,177],"While":[28,72],"existing":[29],"methods":[30,149],"can":[31],"handle":[32,67],"Dirichlet,":[33],"Neumann,":[34],"linear":[36],"Robin":[37],"boundary":[38,41,70,97],"conditions,":[39],"nonlinear":[40,68],"conditions":[42],"arising":[43],"from":[44],"thermal":[45],"radiation":[46,173],"remain":[47],"largely":[48],"unexplored.":[49],"In":[50],"this":[51],"paper,":[52],"we":[53,128],"introduce":[54],"a":[55,88,130,142],"Picard-style":[56],"fixed-point":[57],"iteration":[58],"framework":[59],"that":[60,150],"enables":[61],"radiative":[69],"conditions.":[71],"strict":[73],"theoretical":[74],"convergence":[75],"is":[76],"not":[77],"generally":[78],"guaranteed,":[79],"our":[80,158],"method":[81],"remains":[82],"stable":[83],"empirically":[85],"convergent":[86],"with":[87,94,175],"properly":[89],"chosen":[90],"relaxation":[91],"coefficient.":[92],"Even":[93],"imprecise":[95],"initial":[96],"estimates,":[98,140],"it":[99],"progressively":[100],"approaches":[101],"the":[102,110,120],"correct":[103],"solution.":[104],"Compared":[105],"standard":[107],"linearization":[108],"strategies,":[109],"proposed":[111],"approach":[112,159],"achieves":[113],"significantly":[114],"higher":[115],"accuracy.":[116],"To":[117],"further":[118],"address":[119],"high":[121],"variance":[122,147],"inherent":[123],"estimators,":[127],"propose":[129],"heteroscedastic":[131],"regression-based":[132],"denoising":[133],"technique":[134],"specifically":[135],"designed":[136],"on-boundary":[138],"solution":[139],"filling":[141],"gap":[143],"left":[144],"by":[145],"prior":[146],"reduction":[148],"focus":[151],"solely":[152],"on":[153,163,170],"interior":[154],"points.":[155],"We":[156],"validate":[157],"through":[160],"extensive":[161],"evaluations":[162],"synthetic":[164],"benchmarks":[165],"demonstrate":[167],"its":[168],"effectiveness":[169],"practical":[171],"heat":[172],"simulations":[174]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-25T00:00:00"}
