{"id":"https://openalex.org/W7167080639","doi":"https://doi.org/10.48550/arxiv.2607.00196","title":"TRIE: An Evaluation Framework for Stochastic PDE Surrogates","display_name":"TRIE: An Evaluation Framework for Stochastic PDE Surrogates","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7167080639","doi":"https://doi.org/10.48550/arxiv.2607.00196"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2607.00196","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026412153","display_name":"Bharat Srikishan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Srikishan, Bharat","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139907619","display_name":"Javier E. Santos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santos, Javier E.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074615163","display_name":"Nikhil Muralidhar","orcid":"https://orcid.org/0000-0001-7068-2981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muralidhar, Nikhil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054864021","display_name":"Charles D. Young","orcid":"https://orcid.org/0000-0003-4762-645X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Young, Charles D.","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/T11206","display_name":"Model Reduction and Neural Networks","score":0.2159000039100647,"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":0.2159000039100647,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.21220000088214874,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.09839999675750732,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.5960999727249146},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.45010000467300415},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.41909998655319214},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4041000008583069},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.38580000400543213},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.38019999861717224},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.37229999899864197},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.35499998927116394},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.35370001196861267},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.34630000591278076}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5960999727249146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5781000256538391},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35370001196861267},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.34630000591278076},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3086000084877014},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.3000999987125397},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2985999882221222},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2976999878883362},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C917703","wikidata":"https://www.wikidata.org/wiki/Q7239668","display_name":"Predictive inference","level":5,"score":0.2915000021457672},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2865999937057495},{"id":"https://openalex.org/C2780310539","wikidata":"https://www.wikidata.org/wiki/Q12547192","display_name":"Imperfect","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2825999855995178},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.27799999713897705},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.2775000035762787},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2718000113964081},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2709999978542328},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2607.00196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00196","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"display_name":"Peace, Justice and strong institutions","score":0.6480875611305237,"id":"https://metadata.un.org/sdg/16"}],"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],"scientific":[1],"systems":[2],"exhibit":[3],"uncertainty":[4,106,130],"from":[5],"stochastic":[6,45,75,78,118,195],"forcing,":[7],"unresolved":[8],"degrees":[9],"of":[10,170,194],"freedom,":[11],"or":[12],"imperfect":[13],"observations,":[14],"making":[15],"reliable":[16],"surrogate":[17],"forecasting":[18,197],"fundamentally":[19],"distributional":[20],"rather":[21],"than":[22],"pointwise.":[23],"For":[24],"such":[25,108],"systems,":[26],"deterministic":[27],"neural":[28,91],"surrogates":[29,47,92],"fail":[30],"to":[31,61,100,190],"capture":[32],"statistical":[33,103,172],"measures":[34],"and":[35,59,77,113,124,128,147,186],"forecast":[36],"uncertainty.":[37],"We":[38,65,182],"introduce":[39],"TRIE,":[40],"an":[41],"evaluation":[42,86,193],"framework":[43],"for":[44],"PDE":[46,196],"that":[48,88,160],"asks":[49],"whether":[50],"models":[51,136,163],"reproduce":[52],"invariant":[53,144],"measures,":[54],"provide":[55,137],"trustworthy":[56],"predictive":[57],"uncertainty,":[58],"scale":[60],"efficient":[62],"probabilistic":[63,155],"generation.":[64],"demonstrate":[66],"TRIE":[67],"on":[68],"two":[69],"stationary":[70],"chaotic":[71],"spatially":[72],"extended":[73],"SPDEs,":[74],"Kuramoto--Sivashinsky":[76],"Kolmogorov":[79,176],"flow,":[80],"across":[81],"11":[82],"parameter":[83],"values.":[84],"Our":[85],"shows":[87],"standard":[89],"pointwise-trained":[90],"can":[93],"produce":[94,117],"plausible":[95],"short":[96],"rollouts":[97],"while":[98,174],"failing":[99],"match":[101],"long-time":[102],"structure.":[104],"Approximate":[105],"methods":[107],"as":[109],"Monte":[110],"Carlo":[111],"dropout":[112],"heteroscedastic":[114],"Gaussian":[115],"likelihoods":[116],"forecasts,":[119],"but":[120],"are":[121],"often":[122],"miscalibrated":[123],"overconfident":[125],"under":[126],"temporal":[127],"spatial":[129],"diagnostics.":[131],"Across":[132],"these":[133],"criteria,":[134],"generative":[135,162],"the":[138,149],"most":[139],"consistent":[140],"performance,":[141],"accurately":[142],"capturing":[143],"measure":[145],"statistics":[146],"achieving":[148],"lowest":[150],"CRPS":[151],"in":[152],"all":[153],"reported":[154],"settings.":[156],"Finally,":[157],"we":[158],"show":[159],"latent":[161],"with":[164],"automatic":[165],"dimension":[166],"discovery":[167],"retain":[168],"much":[169],"this":[171],"fidelity":[173],"reducing":[175],"inference":[177],"time":[178],"by":[179],"roughly":[180],"$12\\times$.":[181],"release":[183],"our":[184],"code":[185],"data":[187],"at":[188],"https://github.com/scailab/TRIE-SPDE-Bench":[189],"support":[191],"reproducible":[192],"models.":[198]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}
