{"id":"https://openalex.org/W7163984114","doi":"https://doi.org/10.48550/arxiv.2606.08817","title":"Low-Variance Randomised Numerical Linear Algebra for Finite Element Simulation","display_name":"Low-Variance Randomised Numerical Linear Algebra for Finite Element Simulation","publication_year":2026,"publication_date":"2026-06-07","ids":{"openalex":"https://openalex.org/W7163984114","doi":"https://doi.org/10.48550/arxiv.2606.08817"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.08817","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08817","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":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.2606.08817","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138238016","display_name":"N. Polydorides","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polydorides, N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112007594","display_name":"Yinyin Wu","orcid":"https://orcid.org/0009-0007-5095-2738"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Y.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138282910","display_name":". H. Noori","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Noori, . H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088111198","display_name":"H. Vandierendonck","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vandierendonck, H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138223280","display_name":"R. Woods","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Woods, R.","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":0.5274999737739563,"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":0.5274999737739563,"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":0.11559999734163284,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.10100000351667404,"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/finite-element-method","display_name":"Finite element method","score":0.5475000143051147},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5254999995231628},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.5134999752044678},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.44519999623298645},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4153999984264374},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.41350001096725464},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.39820000529289246},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.3880000114440918},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.3880000114440918},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3815000057220459}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5659999847412109},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5475000143051147},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5254999995231628},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.5134999752044678},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4846999943256378},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.44519999623298645},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.41350001096725464},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3856000006198883},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3815000057220459},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2994999885559082},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.26669999957084656},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.08817","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08817","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":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.2606.08817","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.08817","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"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":{"We":[0,99],"present":[1],"a":[2,49,55,69],"low-variance":[3],"randomised":[4],"numerical":[5],"linear":[6],"algebra":[7],"approach":[8],"for":[9,37,103,174],"multi-query":[10],"finite":[11],"element":[12],"systems":[13],"arising":[14],"from":[15],"parametric":[16],"elliptic":[17],"partial":[18],"differential":[19],"equations":[20,86],"with":[21,48,139],"applications":[22],"to":[23,53,68],"digital":[24],"twins":[25],"and":[26,41,59,92,108,111,165],"online":[27],"model":[28],"calibration.":[29],"The":[30,120],"method":[31,115,158],"relies":[32],"on":[33,116],"Galerkin":[34],"subspace":[35],"projection":[36],"reducing":[38],"the":[39,77,82,89,95,104,114,125,133,140,146,150],"dimensionality,":[40],"then":[42,66,112],"combines":[43],"parameter-oblivious":[44,152],"leverage-score":[45],"Bernoulli":[46],"sampling":[47],"control":[50,136],"variates":[51,137],"scheme":[52],"yield":[54],"reduced-variance":[56],"`forward'":[57],"sketch":[58,63,141],"an":[60],"invertible":[61],"`inverse'":[62],"that":[64,123,171],"are":[65,172],"fused":[67],"single":[70],"efficient":[71],"regularised":[72],"estimator.":[73],"Effectively,":[74],"this":[75,155],"reduces":[76],"computational":[78],"cost":[79],"in":[80,162],"computing":[81],"projected":[83],"system":[84],"of":[85,94,135],"while":[87,167],"preserving":[88],"structure,":[90],"stability,":[91],"accuracy":[93,169],"underlying":[96],"FEM":[97],"formulation.":[98],"derive":[100],"probabilistic":[101],"bounds":[102],"sketching":[105],"error,":[106],"invertibility,":[107],"estimator":[109],"variance,":[110],"validate":[113],"large-scale":[117],"example":[118],"problems.":[119],"results":[121],"show":[122],"when":[124],"parameter":[126],"fields":[127],"do":[128],"not":[129],"vary":[130],"too":[131],"sharply,":[132],"synergy":[134],"together":[138],"fusion":[142],"can":[143],"largely":[144],"offset":[145],"loss":[147],"incurred":[148],"by":[149],"sub-optimal":[151],"sampling.":[153],"In":[154],"regime,":[156],"our":[157],"achieves":[159],"substantial":[160],"savings":[161],"time,":[163],"memory,":[164],"communication":[166],"maintaining":[168],"levels":[170],"acceptable":[173],"scientific":[175],"simulation.":[176]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-10T00:00:00"}
