{"id":"https://openalex.org/W7133689615","doi":"https://doi.org/10.48550/arxiv.2603.03922","title":"Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs","display_name":"Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs","publication_year":2026,"publication_date":"2026-03-04","ids":{"openalex":"https://openalex.org/W7133689615","doi":"https://doi.org/10.48550/arxiv.2603.03922"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.03922","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":"preprint","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/A5125049888","display_name":"Pengyu Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhang, Pengyu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011557874","display_name":"Arnaud Vadeboncoeur","orcid":"https://orcid.org/0000-0003-4124-6763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vadeboncoeur, Arnaud","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074278661","display_name":"Alex Glyn-Davies","orcid":"https://orcid.org/0000-0001-5201-1228"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Glyn-Davies, Alex","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128173590","display_name":"Mark Girolami","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Girolami, Mark","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5125049888"],"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":0.8471999764442444,"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":0.8471999764442444,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.04670000076293945,"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"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.015300000086426735,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6205000281333923},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.491100013256073},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.48080000281333923},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4449999928474426},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4422999918460846},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.435699999332428},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.40139999985694885},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3903999924659729},{"id":"https://openalex.org/keywords/inverse-dynamics","display_name":"Inverse dynamics","score":0.37770000100135803}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6811000108718872},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6205000281333923},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.491100013256073},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4699000120162964},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4449999928474426},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4000999927520752},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C187523126","wikidata":"https://www.wikidata.org/wiki/Q17098330","display_name":"Inverse dynamics","level":3,"score":0.37770000100135803},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.35679998993873596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34700000286102295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3402000069618225},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.3093000054359436},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.2581999897956848},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.03922","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.2603.03922","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.03922","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":"pmh:doi:10.48550/arxiv.2603.03922","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Inverse":[0],"problems":[1],"are":[2],"the":[3,42,57,98,107,112,122,137,149,164,168,176,189,214],"task":[4],"of":[5,40,45,89,102,114,140,158,167,192],"calibrating":[6],"models":[7,25],"to":[8,23,95,206],"match":[9],"data.":[10],"They":[11],"play":[12,64],"a":[13,37,46,81,130,153,159,202,209],"pivotal":[14],"role":[15],"in":[16,111,196],"diverse":[17],"engineering":[18],"applications":[19],"by":[20],"allowing":[21],"practitioners":[22],"align":[24],"with":[26],"reality.":[27],"In":[28,76],"many":[29],"applications,":[30],"engineers":[31],"and":[32,72,105,143,184,221,231],"scientists":[33],"do":[34],"not":[35],"have":[36],"complete":[38,58],"picture":[39],"i)":[41],"detailed":[43],"properties":[44],"system":[47],"(such":[48,65],"as":[49,66],"material":[50],"properties,":[51],"geometry,":[52],"initial":[53],"conditions,":[54],"etc.);":[55],"ii)":[56],"laws":[59],"describing":[60],"all":[61],"dynamics":[62,110],"at":[63],"friction":[67],"laws,":[68],"complicated":[69],"damping":[70],"phenomena,":[71],"general":[73],"nonlinear":[74],"interactions).":[75],"this":[77,172,217],"paper,":[78],"we":[79,128,151,174,200,219],"develop":[80],"principled":[82],"methodology":[83],"for":[84,125,136,182],"leveraging":[85],"data":[86],"from":[87],"collections":[88],"distinct":[90,223],"yet":[91],"related":[92],"physical":[93],"systems":[94,142],"jointly":[96],"estimate":[97,157],"individual":[99],"model":[100,212],"parameters":[101,124],"each":[103,126],"system,":[104,127],"learn":[106,148],"shared":[108],"unknown":[109,123],"form":[113],"an":[115],"ML-based":[116],"closure":[117],"model.":[118],"To":[119,147,170,187],"robustly":[120],"infer":[121],"employ":[129],"hierarchical":[131],"Bayesian":[132],"framework,":[133,218],"which":[134],"allows":[135],"joint":[138],"inference":[139],"multiple":[141],"their":[144],"population-level":[145],"statistics.":[146],"closures,":[150],"use":[152],"maximum":[154],"marginal":[155],"likelihood":[156],"neural":[160],"network":[161],"embeded":[162],"within":[163],"ODE/PDE":[165],"formulation":[166],"problem.":[169],"realize":[171],"framework":[173],"utilize":[175],"ensemble":[177],"Metropolis-Adjusted":[178],"Langevin":[179],"Algorithm":[180],"(MALA)":[181],"stable":[183],"efficient":[185],"sampling.":[186],"mitigate":[188],"computational":[190],"bottleneck":[191],"repetitive":[193],"forward":[194,211],"evaluations":[195],"solving":[197],"inverse":[198],"problems,":[199],"introduce":[201],"bilevel":[203],"optimization":[204],"strategy":[205],"simultaneously":[207],"train":[208],"surrogate":[210,224],"alongside":[213],"inference.":[215],"Within":[216],"evaluate":[220],"compare":[222],"architectures,":[225],"specifically":[226],"Fourier":[227],"Neural":[228,234],"Operators":[229],"(FNO)":[230],"parametric":[232],"Physics-Informed":[233],"Network":[235],"(PINNs).":[236]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-06T00:00:00"}