{"id":"https://openalex.org/W7127182113","doi":"https://doi.org/10.48550/arxiv.2601.22751","title":"Discovering Scaling Exponents with Physics-Informed M\u00fcntz-Sz\u00e1sz Networks","display_name":"Discovering Scaling Exponents with Physics-Informed M\u00fcntz-Sz\u00e1sz Networks","publication_year":2026,"publication_date":"2026-01-30","ids":{"openalex":"https://openalex.org/W7127182113","doi":"https://doi.org/10.48550/arxiv.2601.22751"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2601.22751","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/A5120047919","display_name":"Gnankan Landry Regis N'guessan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N'guessan, Gnankan Landry Regis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5124776153","display_name":"Bum Jun Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Bum Jun","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":0.15010623,"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":0.755299985408783,"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":0.755299985408783,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.1525000035762787,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.052400000393390656,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6686000227928162},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6481999754905701},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.544700026512146},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4700999855995178},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.40380001068115234},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.391400009393692},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.3700999915599823},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.3546999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6743000149726868},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6686000227928162},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6481999754905701},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.544700026512146},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4700999855995178},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41130000352859497},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.40380001068115234},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3700999915599823},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3700999915599823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35679998993873596},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2601.22751","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2601.22751","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.22751","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2601.22751","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.49681535363197327,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Physical":[0],"systems":[1],"near":[2],"singularities,":[3],"interfaces,":[4],"and":[5,43,53,64,82,105,115,143],"critical":[6],"points":[7],"exhibit":[8],"power-law":[9,27],"scaling,":[10],"yet":[11],"standard":[12],"neural":[13,159],"networks":[14,160],"leave":[15],"the":[16,41,59,91,99,156,162],"governing":[17],"exponents":[18,33,66,89,108],"implicit.":[19],"We":[20,47],"introduce":[21],"physics-informed":[22],"M\"untz-Sz'asz":[23],"Networks":[24],"(MSN-PINN),":[25],"a":[26,119,125],"basis":[28],"network":[29],"that":[30],"treats":[31],"scaling":[32,45],"as":[34,68,139],"trainable":[35],"parameters.":[36],"The":[37],"model":[38],"outputs":[39],"both":[40],"solution":[42],"its":[44],"structure.":[46],"prove":[48],"identifiability,":[49],"or":[50],"unique":[51],"recovery,":[52],"show":[54],"that,":[55],"under":[56,80],"these":[57],"conditions,":[58],"squared":[60],"error":[61,79],"between":[62],"learned":[63,169],"true":[65],"scales":[67],"$O(|\u03bc-":[69],"\u03b1|^2)$.":[70],"Across":[71],"experiments,":[72],"MSN-PINN":[73,167],"achieves":[74],"single-exponent":[75],"recovery":[76],"with":[77,95,113,129,161,171],"1--5%":[78],"noise":[81],"sparse":[83],"sampling.":[84],"It":[85],"recovers":[86,106],"corner":[87],"singularity":[88],"for":[90],"two-dimensional":[92],"Laplace":[93],"equation":[94],"0.009%":[96],"error,":[97],"matches":[98],"classical":[100],"result":[101],"of":[102,149,158,164],"Kondrat'ev":[103],"(1967),":[104],"forcing-induced":[107],"in":[109],"singular":[110],"Poisson":[111],"problems":[112],"0.03%":[114],"0.05%":[116],"errors.":[117],"On":[118],"40-configuration":[120],"wedge":[121],"benchmark,":[122],"it":[123],"reaches":[124],"100%":[126],"success":[127],"rate":[128],"0.022%":[130],"mean":[131],"error.":[132],"Constraint-aware":[133],"training":[134],"encodes":[135],"physical":[136,173],"requirements":[137],"such":[138],"boundary":[140],"condition":[141],"compatibility":[142],"improves":[144],"accuracy":[145],"by":[146],"three":[147],"orders":[148],"magnitude":[150],"over":[151],"naive":[152],"training.":[153],"By":[154],"combining":[155],"expressiveness":[157],"interpretability":[163],"asymptotic":[165],"analysis,":[166],"produces":[168],"parameters":[170],"direct":[172],"meaning.":[174]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-03T00:00:00"}