{"id":"https://openalex.org/W7155160438","doi":"https://doi.org/10.48550/arxiv.2604.19165","title":"Analytical Extraction of Conditional Sobol' Indices via Basis Decomposition of Polynomial Chaos Expansions","display_name":"Analytical Extraction of Conditional Sobol' Indices via Basis Decomposition of Polynomial Chaos Expansions","publication_year":2026,"publication_date":"2026-04-21","ids":{"openalex":"https://openalex.org/W7155160438","doi":"https://doi.org/10.48550/arxiv.2604.19165"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.19165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19165","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.2604.19165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134242744","display_name":"Shijie Zhong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong, Shijie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134253266","display_name":"Jiangfeng Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Jiangfeng","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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.0008999999845400453,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.8198000192642212},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6421999931335449},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5645999908447266},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.48590001463890076},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.448199987411499},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.43720000982284546},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4361000061035156},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4268999993801117},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42489999532699585}],"concepts":[{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.8198000192642212},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6421999931335449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6333000063896179},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5645999908447266},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5454999804496765},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.48590001463890076},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43720000982284546},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35740000009536743},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3472999930381775},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.3172999918460846},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.30809998512268066},{"id":"https://openalex.org/C127436580","wikidata":"https://www.wikidata.org/wiki/Q6452866","display_name":"Polynomial expansion","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.28949999809265137},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C174920663","wikidata":"https://www.wikidata.org/wiki/Q5159256","display_name":"Conditional dependence","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.19165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19165","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.2604.19165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19165","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":{"In":[0],"uncertainty":[1],"quantification,":[2],"evaluating":[3],"sensitivity":[4,131],"measures":[5],"under":[6,104],"specific":[7],"conditions":[8],"(i.e.,":[9],"conditional":[10,62,105,113,130],"Sobol'":[11,63,116],"indices)":[12],"is":[13,36],"essential":[14],"for":[15,51,112,123],"systems":[16],"with":[17],"parameterized":[18],"responses,":[19],"such":[20],"as":[21],"spatial":[22],"fields":[23,91],"or":[24,126],"varying":[25],"operating":[26],"conditions.":[27],"Traditional":[28],"approaches":[29],"often":[30],"rely":[31],"on":[32,94,99],"point-wise":[33,160],"modeling,":[34],"which":[35],"computationally":[37],"expensive":[38],"and":[39,115,149,154],"may":[40],"lack":[41],"consistency":[42],"across":[43],"the":[44,60,74,82,95,100,121,143],"parameter":[45],"space.":[46],"This":[47,118],"paper":[48],"demonstrates":[49],"that":[50,92,142],"a":[52,86,134],"pre-trained":[53],"global":[54,83],"Polynomial":[55],"Chaos":[56],"Expansion":[57],"(PCE)":[58],"model,":[59],"analytical":[61,89],"indices":[64],"are":[65],"inherently":[66],"embedded":[67],"within":[68],"its":[69],"basis":[70],"functions.":[71],"By":[72],"leveraging":[73],"tensor-product":[75],"property":[76],"of":[77,88,102],"PCE":[78],"bases,":[79],"we":[80,108],"reformulate":[81],"expansion":[84],"into":[85,133],"set":[87],"coefficient":[90],"depend":[93],"conditioning":[96],"variables.":[97],"Based":[98],"preservation":[101],"orthogonality":[103],"probability":[106],"measures,":[107],"derive":[109],"closed-form":[110],"expressions":[111],"variances":[114],"indices.":[117],"framework":[119],"bypasses":[120],"need":[122],"repetitive":[124],"modeling":[125],"additional":[127],"sampling,":[128],"transforming":[129],"analysis":[132],"purely":[135],"algebraic":[136],"post-processing":[137],"step.":[138],"Numerical":[139],"benchmarks":[140],"indicate":[141],"proposed":[144],"method":[145],"ensures":[146],"physical":[147],"coherence":[148],"offers":[150],"superior":[151],"numerical":[152],"robustness":[153],"computational":[155],"efficiency":[156],"compared":[157],"to":[158],"conventional":[159],"approaches.":[161]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-23T00:00:00"}