{"id":"https://openalex.org/W7147033476","doi":"https://doi.org/10.48550/arxiv.2603.29249","title":"A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs","display_name":"A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7147033476","doi":"https://doi.org/10.48550/arxiv.2603.29249"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.29249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29249","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2603.29249","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049820569","display_name":"Wei-Fan Hu","orcid":"https://orcid.org/0000-0002-0489-8458"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hu, Wei-Fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132611283","display_name":"Shi-Xiang Zhong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong, Shi-Xiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008764613","display_name":"Po\u2010Wen Hsieh","orcid":"https://orcid.org/0000-0001-8235-7393"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hsieh, Po-Wen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132650376","display_name":"Chung-Kai Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Chung-Kai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132558773","display_name":"Te-Sheng Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Te-Sheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5049820569"],"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":0.4968000054359436,"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":0.4968000054359436,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.16820000112056732,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.08399999886751175,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/scalar","display_name":"Scalar (mathematics)","score":0.6044999957084656},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.5728999972343445},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5400999784469604},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5123999714851379},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4765999913215637},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.46970000863075256},{"id":"https://openalex.org/keywords/method-of-matched-asymptotic-expansions","display_name":"Method of matched asymptotic expansions","score":0.38519999384880066},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.38179999589920044},{"id":"https://openalex.org/keywords/magnetohydrodynamic-drive","display_name":"Magnetohydrodynamic drive","score":0.37880000472068787}],"concepts":[{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6044999957084656},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.5728999972343445},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5123999714851379},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4684999883174896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4251999855041504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.398499995470047},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.38519999384880066},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.38179999589920044},{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.37880000472068787},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32600000500679016},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32100000977516174},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.30570000410079956},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C23221634","wikidata":"https://www.wikidata.org/wiki/Q4925317","display_name":"Blasius boundary layer","level":4,"score":0.2671999931335449},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.29249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29249","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.29249","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.29249","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.46638378500938416}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Singularly":[0],"perturbed":[1],"partial":[2],"differential":[3],"equations":[4],"arise":[5],"in":[6,63],"many":[7],"applications,":[8],"including":[9],"magnetohydrodynamic":[10],"duct":[11],"flows,":[12],"chemical":[13],"reaction":[14,133,138],"transport":[15],"systems,":[16,139],"and":[17,29,58,119,131,135,143],"Poisson":[18],"Boltzmann":[19],"electrostatics.":[20],"These":[21],"problems":[22],"are":[23,106],"characterized":[24],"by":[25],"sharp":[26],"boundary":[27,98,103,150],"layers":[28],"pronounced":[30],"multiscale":[31],"behavior,":[32],"posing":[33],"significant":[34],"challenges":[35],"for":[36,149],"numerical":[37],"methods.":[38],"Existing":[39],"approaches,":[40],"particularly":[41],"machine":[42],"learning":[43,73],"based":[44,75],"methods,":[45],"often":[46],"rely":[47],"on":[48,76,128,141],"explicit":[49],"asymptotic":[50],"decompositions":[51],"or":[52],"specialized":[53],"architectures,":[54],"increasing":[55],"implementation":[56],"complexity":[57],"leading":[59],"to":[60],"optimization":[61],"imbalance":[62],"stiff":[64],"regimes.":[65],"In":[66],"this":[67],"work,":[68],"we":[69],"propose":[70],"a":[71,77],"unified":[72],"framework":[74],"weighted":[78],"loss":[79],"formulation":[80,113],"within":[81],"the":[82,97,102],"standard":[83],"physics":[84],"informed":[85],"neural":[86],"network":[87],"setting.":[88],"The":[89,111],"proposed":[90],"method":[91],"requires":[92],"only":[93],"prior":[94],"knowledge":[95],"of":[96],"layer":[99,104,151],"thickness,":[100],"while":[101,157],"locations":[105],"automatically":[107],"identified":[108],"during":[109],"training.":[110],"resulting":[112],"avoids":[114],"problem":[115],"specific":[116],"architectural":[117],"modifications":[118],"remains":[120],"applicable":[121],"across":[122],"different":[123],"equation":[124],"types.":[125],"Numerical":[126],"experiments":[127],"both":[129],"scalar":[130],"coupled":[132],"diffusion":[134,137],"convection":[136],"defined":[140],"regular":[142],"irregular":[144],"domains,":[145],"demonstrate":[146],"robust":[147],"performance":[148],"thickness":[152],"as":[153,155],"small":[154],"$10^{-10}$":[156],"maintaining":[158],"high":[159],"solution":[160],"accuracy.":[161]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-04-02T00:00:00"}