{"id":"https://openalex.org/W7213608749","doi":"https://doi.org/10.48550/arxiv.2609.20814","title":"How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?","display_name":"How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213608749","doi":"https://doi.org/10.48550/arxiv.2609.20814"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20814","pdf_url":"https://arxiv.org/pdf/2609.20814","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.20814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119832263","display_name":"Pochinapeddi Sai Bhargav","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhargav, Pochinapeddi Sai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114617905","display_name":"Nithin Somasekharan","orcid":"https://orcid.org/0009-0007-1186-8496","observed_orcids":["https://orcid.org/0009-0007-1186-8496"]},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Somasekharan, Nithin","raw_affiliation_strings":["Rensselaer Polytechnic Institute Troy , NY 12180"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rensselaer Polytechnic Institute Troy , NY 12180","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099437733","display_name":"Rohit Sunil Kanchi","orcid":"https://orcid.org/0009-0005-4718-3101","observed_orcids":["https://orcid.org/0009-0005-4718-3101"]},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kanchi, Rohit Sunil","raw_affiliation_strings":["University of Tennessee Knoxville , TN 37996"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tennessee Knoxville , TN 37996","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152115928","display_name":"Sicheng He","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"He, Sicheng","raw_affiliation_strings":["University of Tennessee Knoxville , TN 37996"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tennessee Knoxville , TN 37996","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151747499","display_name":"Shaowu Pan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pan, Shaowu","raw_affiliation_strings":["Rensselaer Polytechnic Institute Troy , NY 12180"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rensselaer Polytechnic Institute Troy , NY 12180","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9980000257492065,"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":0.9980000257492065,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.00019999999494757503,"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/distribution-shift","display_name":"distribution shift","score":0.7839999794960022},{"id":"https://openalex.org/keywords/pretraining","display_name":"pre-training","score":0.7519999742507935},{"id":"https://openalex.org/keywords/physics-informed-neural-networks","display_name":"physics-informed neural networks","score":0.7490000128746033},{"id":"https://openalex.org/keywords/cfd-surrogate-model","display_name":"CFD surrogate model","score":0.6140000224113464},{"id":"https://openalex.org/keywords/rans-turbulence-modeling","display_name":"RANS turbulence models","score":0.6850000023841858},{"id":"https://openalex.org/keywords/spalart-allmaras-turbulence-model","display_name":"Spalart-Allmaras turbulence model","score":0.9629999995231628},{"id":"https://openalex.org/keywords/airfoil-aerodynamics","display_name":"airfoil aerodynamics","score":0.5879999995231628},{"id":"https://openalex.org/keywords/fine-tuning","display_name":"fine-tuning","score":0.8109999895095825},{"id":"https://openalex.org/keywords/data-coverage","display_name":"data coverage","score":0.49799999594688416},{"id":"https://openalex.org/keywords/transition-modeling","display_name":"transition modeling","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C112124176","wikidata":"https://www.wikidata.org/wiki/Q4698744","display_name":"Airfoil","level":2,"score":0.8604000210762024},{"id":"https://openalex.org/C2776911258","wikidata":"https://www.wikidata.org/wiki/Q5501170","display_name":"Freestream","level":4,"score":0.6642000079154968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5250999927520752},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C32526432","wikidata":"https://www.wikidata.org/wiki/Q1536235","display_name":"Reynolds-averaged Navier\u2013Stokes equations","level":3,"score":0.4368000030517578},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3788999915122986},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36070001125335693},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3537999987602234},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C2781235140","wikidata":"https://www.wikidata.org/wiki/Q275131","display_name":"Scratch","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3239000141620636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30630001425743103},{"id":"https://openalex.org/C1633027","wikidata":"https://www.wikidata.org/wiki/Q815820","display_name":"Computational fluid dynamics","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2903999984264374},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2883000075817108},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20814","pdf_url":"https://arxiv.org/pdf/2609.20814","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.20814","doi":"https://doi.org/10.48550/arxiv.2609.20814","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20814","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.20814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20814","pdf_url":"https://arxiv.org/pdf/2609.20814","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213608749.pdf","grobid_xml":"https://content.openalex.org/works/W7213608749.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W3094502228","https://openalex.org/W4304207712","https://openalex.org/W4402916309","https://openalex.org/W4414588894","https://openalex.org/W4415795327","https://openalex.org/W4415796935"],"related_works":["https://openalex.org/W7220913144","https://openalex.org/W4416554874","https://openalex.org/W7221754804","https://openalex.org/W7220358625","https://openalex.org/W4417095900","https://openalex.org/W7148932850","https://openalex.org/W4416952962","https://openalex.org/W7196965432","https://openalex.org/W4409486766","https://openalex.org/W4389298155"],"abstract_inverted_index":{"Pretraining":[0],"a":[1,35,49,81],"neural":[2],"PDE":[3],"surrogate":[4,36],"can":[5],"reduce":[6],"the":[7,60,74,78,92,100,125,129,134],"amount":[8],"of":[9,27,80],"new":[10,50],"CFD":[11],"data":[12],"needed":[13],"when":[14],"geometry":[15],"or":[16],"modeled":[17,161],"physics":[18],"changes.":[19],"However,":[20],"it":[21,47],"remains":[22],"unclear":[23],"how":[24],"different":[25],"components":[26],"distribution":[28],"shift":[29],"affect":[30],"this":[31,105],"benefit.":[32],"We":[33],"pretrain":[34],"on":[37,48,86,119,149],"254,909":[38],"RANS":[39],"solutions":[40],"from":[41,84],"one":[42],"airfoil":[43],"family":[44,51],"and":[45,65,154,157],"fine-tune":[46],"under":[52],"two":[53],"target":[54,127,158],"settings":[55],"with":[56,67],"matched":[57],"freestream":[58],"ranges:":[59],"same":[61],"Spalart-Allmaras":[62],"(SA)":[63],"modeling":[64],"SA":[66],"added":[68],"$e^N$":[69],"transition":[70],"modeling.":[71],"At":[72,111],"$N=1000$,":[73,112],"pretrained":[75],"model":[76,82],"matches":[77],"accuracy":[79],"trained":[83],"scratch":[85],"$3.25\\times$":[87],"as":[88,97],"many":[89,98],"samples":[90],"for":[91,99,124],"same-SA":[93,126],"target,":[94],"but":[95,122],"$2.58\\times$":[96],"transition-modeled":[101],"target.":[102],"By":[103],"$N=5000$,":[104],"ordering":[106],"reverses":[107],"($1.56\\times$":[108],"versus":[109],"$1.86\\times$).":[110],"sampling":[113],"more":[114],"distinct":[115],"airfoils":[116],"lowers":[117],"error":[118],"both":[120],"targets,":[121],"only":[123],"is":[128],"gain":[130],"increase":[131],"larger":[132],"than":[133],"observed":[135],"draw-to-draw":[136],"variation":[137],"($3.3\\times$":[138],"to":[139],"$4.0\\times$).":[140],"These":[141],"results":[142],"show":[143],"that":[144],"pretraining":[145],"value":[146],"depends":[147],"jointly":[148],"target-data":[150,152],"budget,":[151],"coverage,":[153],"whether":[155],"source":[156],"differ":[159],"in":[160],"physics.":[162]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}
