{"id":"https://openalex.org/W7164200162","doi":"https://doi.org/10.48550/arxiv.2606.09949","title":"Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training","display_name":"Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training","publication_year":2026,"publication_date":"2026-06-08","ids":{"openalex":"https://openalex.org/W7164200162","doi":"https://doi.org/10.48550/arxiv.2606.09949"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05646322v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05646322","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-05646322","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138358319","display_name":"Pierre Cesar","orcid":null},"institutions":[{"id":"https://openalex.org/I4405259361","display_name":"DATAMOVE: Mouvements de donn\u00e9es pour le calcul haute performance","ror":"https://ror.org/024cwyh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I4405259361","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cesar, Pierre","raw_affiliation_strings":["DATAMOVE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DATAMOVE","institution_ids":["https://openalex.org/I4405259361"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093367439","display_name":"Sofya Dymchenko","orcid":null},"institutions":[{"id":"https://openalex.org/I4405259361","display_name":"DATAMOVE: Mouvements de donn\u00e9es pour le calcul haute performance","ror":"https://ror.org/024cwyh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I4405259361","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dymchenko, Sofya","raw_affiliation_strings":["DATAMOVE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DATAMOVE","institution_ids":["https://openalex.org/I4405259361"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138329950","display_name":"Abhishek Purandare","orcid":null},"institutions":[{"id":"https://openalex.org/I4405259361","display_name":"DATAMOVE: Mouvements de donn\u00e9es pour le calcul haute performance","ror":"https://ror.org/024cwyh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I4405259361","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Purandare, Abhishek","raw_affiliation_strings":["DATAMOVE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DATAMOVE","institution_ids":["https://openalex.org/I4405259361"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074769385","display_name":"Bruno Raffin","orcid":"https://orcid.org/0000-0002-7980-4946"},"institutions":[{"id":"https://openalex.org/I4405259361","display_name":"DATAMOVE: Mouvements de donn\u00e9es pour le calcul haute performance","ror":"https://ror.org/024cwyh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I4210101348","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I4405259361","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Raffin, Bruno","raw_affiliation_strings":["DATAMOVE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DATAMOVE","institution_ids":["https://openalex.org/I4405259361"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4405259361"],"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":0.7307999730110168,"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":0.7307999730110168,"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":0.11890000104904175,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.052799999713897705,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5576000213623047},{"id":"https://openalex.org/keywords/surrogate-model","display_name":"Surrogate model","score":0.48579999804496765},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.47049999237060547},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4575999975204468},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.41839998960494995},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4178999960422516},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4007999897003174},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.39010000228881836},{"id":"https://openalex.org/keywords/training-set","display_name":"Training set","score":0.3885999917984009}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6474999785423279},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5576000213623047},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5228000283241272},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5098000168800354},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.48579999804496765},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.47049999237060547},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C122048520","wikidata":"https://www.wikidata.org/wiki/Q2913954","display_name":"Percentile","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.37790000438690186},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C190839683","wikidata":"https://www.wikidata.org/wiki/Q2448197","display_name":"Train","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C2777851325","wikidata":"https://www.wikidata.org/wiki/Q7094102","display_name":"Online model","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3416999876499176},{"id":"https://openalex.org/C2781395549","wikidata":"https://www.wikidata.org/wiki/Q4680762","display_name":"Adaptive sampling","level":3,"score":0.3334999978542328},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.329800009727478},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2944999933242798},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C142806159","wikidata":"https://www.wikidata.org/wiki/Q7646876","display_name":"Surrogate data","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05646322v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05646322","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2606.09949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09949","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":"pmh:oai:HAL:hal-05646322v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-05646322","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"info:eu-repo/semantics/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":{"Data-driven":[0],"PDE":[1,10,25],"surrogates":[2,236],"are":[3,72],"trained":[4,62,235],"with":[5,178,226,237],"data":[6,67,162],"produced":[7],"by":[8,78],"numerical":[9],"solvers.":[11],"However,":[12],"when":[13],"the":[14,61,105,115,127,169,208],"surrogate's":[15],"goal":[16],"is":[17,38],"to":[18,52,82,113,126,129,144,187,216],"generalize":[19],"across":[20,175],"a":[21,34,75,120,132,136,153,224],"wide":[22],"range":[23],"of":[24,42,234],"configurations":[26],"(e.g.,":[27,140],"initial":[28],"conditions":[29],"and":[30,56,69,110,185,211],"physical":[31],"coefficients),":[32],"generating":[33],"representative":[35],"training":[36,71,170],"set":[37],"non-trivial.":[39],"Uniform":[40],"sampling":[41,116],"configuration":[43,108,145],"parameters":[44,81,109],"often":[45],"under-represents":[46],"trajectories":[47,222],"exhibiting":[48],"challenging":[49,165,180,221],"dynamics,":[50],"leading":[51],"high":[53,157],"prediction":[54],"errors":[55,206],"large":[57],"error":[58,213],"variance":[59],"in":[60,124,205],"surrogate.":[63],"Online":[64,93],"training,":[65],"where":[66],"generation":[68,163],"surrogate":[70,111,128,192],"coupled,":[73],"offers":[74],"natural":[76],"advantage":[77],"allowing":[79],"solver":[80],"be":[83],"steered":[84],"on-the-fly.":[85],"To":[86],"efficiently":[87],"exploit":[88],"this":[89],"capability,":[90],"we":[91],"introduce":[92],"Generative":[94],"Active":[95],"Sampling":[96],"(OGAS),":[97],"an":[98],"active":[99],"learning":[100],"method":[101],"that":[102],"reactively":[103],"learns":[104],"relationship":[106],"between":[107],"performance":[112],"control":[114],"distribution.":[117],"OGAS":[118,159,174,197,229],"trains":[119],"fast":[121],"diffusion":[122],"model":[123],"parallel":[125],"act":[130],"as":[131],"conditional":[133],"sampler,":[134],"mapping":[135],"surrogate-derived":[137],"difficulty":[138],"signal":[139],"loss":[141],"or":[142],"uncertainty)":[143],"parameters.":[146],"By":[147],"actively":[148],"drawing":[149],"target":[150],"signals":[151],"from":[152],"prior":[154],"biased":[155],"toward":[156,164],"difficulty,":[158],"continuously":[160],"steers":[161],"regimes":[166],"without":[167],"delaying":[168],"workflow.":[171],"We":[172],"evaluate":[173],"2D":[176],"PDEs":[177],"distinct":[179],"dynamics":[181],"(Kuramoto-Sivashinsky,":[182],"Navier-Stokes,":[183],"Gray-Scott)":[184],"up":[186],"308":[188],"parameters,":[189],"using":[190],"multiple":[191],"architectures.":[193],"Across":[194],"all":[195],"settings,":[196],"consistently":[198],"improves":[199],"tail":[200],"statistics,":[201],"yielding":[202],"substantial":[203],"reductions":[204],"above":[207],"99th":[209],"percentile":[210],"overall":[212],"dispersion":[214],"compared":[215],"uniform":[217],"sampling.":[218],"While":[219],"prioritizing":[220],"introduces":[223],"trade-off":[225],"average":[227],"error,":[228],"effectively":[230],"ensures":[231],"worst-case":[232],"reliability":[233],"negligible":[238],"wall-time":[239],"overhead.":[240]},"counts_by_year":[],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2026-06-11T00:00:00"}