{"id":"https://openalex.org/W7133311464","doi":"https://doi.org/10.48550/arxiv.2603.00290","title":"Scalable Gaussian process modeling of parametrized spatio-temporal fields","display_name":"Scalable Gaussian process modeling of parametrized spatio-temporal fields","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133311464","doi":"https://doi.org/10.48550/arxiv.2603.00290"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00290","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00290","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.00290","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005799895","display_name":"Srinath Dama","orcid":"https://orcid.org/0000-0002-0538-1258"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dama, Srinath","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112276974","display_name":"Prasanth B Nair","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nair, Prasanth B.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005799895"],"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.7498999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.7498999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.10180000215768814,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.0502999983727932,"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/kronecker-product","display_name":"Kronecker product","score":0.6557000279426575},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5548999905586243},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5512999892234802},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.499099999666214},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.48539999127388},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46140000224113464},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.43050000071525574},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.3937000036239624},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.38449999690055847},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.3797000050544739}],"concepts":[{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.6557000279426575},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5512999892234802},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5303000211715698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5078999996185303},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.499099999666214},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.48539999127388},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46140000224113464},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4300000071525574},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34779998660087585},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29100000858306885},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.26669999957084656},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C131675550","wikidata":"https://www.wikidata.org/wiki/Q7646884","display_name":"Surrogate model","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00290","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00290","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":"doi:10.48550/arxiv.2603.00290","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00290","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":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":{"We":[0,43],"introduce":[1],"a":[2,28,50,112],"scalable":[3,106],"Gaussian":[4],"process":[5],"(GP)":[6],"framework":[7,26,158],"with":[8,55,61,125],"deep":[9,135],"product":[10],"kernels":[11],"for":[12,94,101,163,173],"data-driven":[13,164],"learning":[14,127],"of":[15,38,65,72,79,114,149],"parametrized":[16],"spatio-temporal":[17,35,66],"fields":[18],"over":[19],"fixed":[20],"or":[21],"parameter-dependent":[22],"domains.":[23],"The":[24],"proposed":[25,120,157],"learns":[27],"continuous":[29],"representation,":[30],"enabling":[31,105],"predictions":[32],"at":[33,83],"arbitrary":[34],"coordinates,":[36],"independent":[37],"the":[39,62,76,80,85,90,119,139,147,156],"training":[40,53],"data":[41],"resolution.":[42],"leverage":[44],"Kronecker":[45],"matrix":[46],"algebra":[47],"to":[48],"formulate":[49],"computationally":[51],"efficient":[52,77],"procedure":[54],"complexity":[56],"that":[57,118],"scales":[58],"nearly":[59],"linearly":[60],"total":[63],"number":[64],"grid":[67],"points.":[68],"A":[69],"key":[70],"feature":[71],"our":[73,144],"approach":[74],"is":[75],"computation":[78],"posterior":[81,91],"variance":[82],"essentially":[84],"same":[86],"computational":[87],"cost":[88],"as":[89,130,159],"mean":[92],"(exactly":[93],"Cartesian":[95],"grids":[96],"and":[97,134],"via":[98],"rigorous":[99],"bounds":[100],"unstructured":[102],"grids),":[103],"thereby":[104],"uncertainty":[107,169],"quantification.":[108],"Numerical":[109],"studies":[110],"on":[111],"range":[113],"benchmark":[115],"problems":[116],"demonstrate":[117],"method":[121,145],"achieves":[122],"accuracy":[123,148],"competitive":[124],"operator":[126,136],"methods":[128],"such":[129],"Fourier":[131],"neural":[132],"operators":[133],"networks.":[137],"On":[138],"one-dimensional":[140],"unsteady":[141],"Burgers'":[142],"equation,":[143],"surpasses":[146],"projection-based":[150],"reduced-order":[151],"models.":[152],"These":[153],"results":[154],"establish":[155],"an":[160],"effective":[161],"tool":[162],"surrogate":[165],"modeling,":[166],"particularly":[167],"when":[168],"estimates":[170],"are":[171],"required":[172],"downstream":[174],"tasks.":[175]},"counts_by_year":[],"updated_date":"2026-03-04T07:09:34.246503","created_date":"2026-03-04T00:00:00"}