{"id":"https://openalex.org/W7162674322","doi":"https://doi.org/10.48550/arxiv.2605.28076","title":"Diagnosing the conditional-mean barrier in scientific machine-learning surrogates","display_name":"Diagnosing the conditional-mean barrier in scientific machine-learning surrogates","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162674322","doi":"https://doi.org/10.48550/arxiv.2605.28076"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.28076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28076","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.2605.28076","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137309008","display_name":"Junfeng Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Junfeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5137309008"],"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":0.42660000920295715,"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":0.42660000920295715,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.2687000036239624,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.059300001710653305,"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/unobservable","display_name":"Unobservable","score":0.6661999821662903},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5781999826431274},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.47029998898506165},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.44859999418258667},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4108000099658966},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.39070001244544983},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.3709000051021576},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.3653999865055084},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.36070001125335693},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.35830000042915344}],"concepts":[{"id":"https://openalex.org/C2780695315","wikidata":"https://www.wikidata.org/wiki/Q3799040","display_name":"Unobservable","level":2,"score":0.6661999821662903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.618399977684021},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5781999826431274},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4108000099658966},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3452000021934509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3449000120162964},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34209999442100525},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30880001187324524},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.29339998960494995},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C103982235","wikidata":"https://www.wikidata.org/wiki/Q7309594","display_name":"Regular conditional probability","level":4,"score":0.28459998965263367},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2678000032901764},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.28076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28076","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.2605.28076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.28076","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":{"Many":[0],"prediction":[1],"tasks":[2],"in":[3,40,64,175],"computational":[4],"science":[5],"and":[6,13,56,74,111,154,177],"engineering":[7],"become":[8],"one-to-many":[9],"after":[10],"coarse":[11],"graining":[12],"partial":[14],"observation.":[15],"In":[16,45],"such":[17],"settings,":[18],"deterministic":[19,79,168],"surrogates":[20],"trained":[21],"by":[22,100],"squared":[23,94],"loss":[24,132],"may":[25],"learn":[26],"a":[27,58,89,124,143,150,155,179],"well-defined":[28],"mathematical":[29],"object,":[30],"the":[31,37,41,53,103,106,113,117,131,138,162,165],"conditional":[32,43,83,118,139],"mean,":[33],"while":[34],"still":[35],"missing":[36],"task-relevant":[38],"variability":[39,129],"underlying":[42],"law.":[44],"this":[46,50],"work,":[47],"we":[48],"formulate":[49],"limitation":[51],"as":[52],"conditional-mean":[54],"barrier":[55],"develop":[57],"diagnostic":[59,163],"framework":[60,70],"for":[61],"identifying":[62],"it":[63],"fitted":[65],"scientific":[66],"machine-learning":[67],"surrogates.":[68],"The":[69,120],"combines":[71],"residual-feature":[72],"orthogonality":[73],"effect-size":[75],"diagnostics":[76],"to":[77,116],"distinguish":[78],"underfitting":[80],"from":[81],"irreducible":[82],"variability.":[84,188],"We":[85],"also":[86],"make":[87],"explicit":[88],"simple":[90],"consequence":[91],"of":[92,137],"paired":[93],"loss:":[95],"stochastic":[96],"outputs":[97],"do":[98],"not":[99],"themselves":[101],"overcome":[102],"barrier,":[104,166],"because":[105],"objective":[107],"penalizes":[108],"model":[109,183],"variance":[110],"drives":[112],"predictor":[114],"back":[115],"mean.":[119],"diagnosis":[121],"therefore":[122],"yields":[123],"modeling":[125],"prescription:":[126],"when":[127],"residual":[128],"matters,":[130],"must":[133],"score":[134],"richer":[135],"features":[136],"law":[140,153],"rather":[141],"than":[142],"point":[144],"prediction.":[145],"Reproducible":[146],"numerical":[147],"studies":[148],"on":[149],"controlled":[151],"two-branch":[152],"two-scale":[156],"Lorenz-96":[157],"closure":[158],"problem":[159],"show":[160],"how":[161,167,178],"identifies":[164],"closures":[169],"can":[170,184],"suppress":[171],"collective":[172],"fluctuation":[173],"statistics":[174],"rollout,":[176],"minimal":[180],"likelihood-based":[181],"stochastic-scale":[182],"recover":[185],"substantially":[186],"more":[187]},"counts_by_year":[],"updated_date":"2026-07-08T06:17:01.165560","created_date":"2026-05-29T00:00:00"}
