{"id":"https://openalex.org/W7164503954","doi":"https://doi.org/10.48550/arxiv.2606.13063","title":"A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems","display_name":"A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164503954","doi":"https://doi.org/10.48550/arxiv.2606.13063"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.13063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2606.13063","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092616600","display_name":"Guglielmo Padula","orcid":"https://orcid.org/0009-0005-5269-3296"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Padula, Guglielmo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138546330","display_name":"Michele Girfoglio","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Girfoglio, Michele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138512858","display_name":"Gianluigi Rozza","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rozza, Gianluigi","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":0.6934999823570251,"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":0.6934999823570251,"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":0.23819999396800995,"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":0.012900000438094139,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6725999712944031},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5881999731063843},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5702999830245972},{"id":"https://openalex.org/keywords/dynamic-mode-decomposition","display_name":"Dynamic mode decomposition","score":0.5512999892234802},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5418000221252441},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49549999833106995},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.47429999709129333},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.43140000104904175}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6725999712944031},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5881999731063843},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5702999830245972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5598999857902527},{"id":"https://openalex.org/C2777032711","wikidata":"https://www.wikidata.org/wiki/Q5318993","display_name":"Dynamic mode decomposition","level":2,"score":0.5512999892234802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.54830002784729},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5418000221252441},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49549999833106995},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.47429999709129333},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4560999870300293},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.359499990940094},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.35179999470710754},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.3515999913215637},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.34290000796318054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32199999690055847},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.287200003862381},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.257099986076355},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.13063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.13063","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13063","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"Forecasting":[0],"the":[1,22,93,112,117,133,178,181],"evolution":[2],"of":[3,170,180],"complex":[4,70,191],"dynamical":[5,71,192],"systems":[6,72,193],"remains":[7],"a":[8,66,74,184],"fundamentally":[9],"challenging":[10],"task,":[11],"primarily":[12],"due":[13],"to":[14,51,111],"pronounced":[15],"nonlinear":[16],"interactions,":[17],"high-dimensional":[18],"state":[19],"spaces,":[20],"and":[21,27,45,47,85,107,128,162,164,186],"concomitant":[23],"requirement":[24],"for":[25,68,131,189],"rigorous":[26,195],"reliable":[28],"uncertainty":[29,105,196],"quantification.":[30,197],"Contemporary":[31],"reduced-order":[32,126],"modelling":[33,127],"(ROM)":[34],"frameworks":[35],"frequently":[36],"exhibit":[37],"inherent":[38],"trade-offs":[39],"among":[40,56],"predictive":[41],"accuracy,":[42],"numerical":[43],"stability,":[44],"interpretability,":[46],"thus":[48],"often":[49],"fail":[50],"achieve":[52],"an":[53],"optimal":[54],"balance":[55],"these":[57,62],"competing":[58],"objectives.":[59],"To":[60],"address":[61],"limitations,":[63],"we":[64],"propose":[65],"framework":[67,182],"forecasting":[69,103,149,190],"via":[73],"kernel":[75],"autonomous":[76,114],"ordinary":[77],"differential":[78],"equation":[79,115],"approach":[80],"based":[81],"on":[82],"Gaussian":[83,94],"Processes":[84],"Quadratic":[86],"Order":[87],"Model":[88],"Reduction.":[89],"Our":[90],"base":[91],"method,":[92],"Process":[95],"Ordinary":[96],"Differential":[97],"Equations":[98],"model,":[99],"allows":[100],"accurate":[101],"short-term":[102],"with":[104,123,194],"quantification,":[106],"it":[108,122],"provably":[109],"converges":[110],"real":[113],"in":[116,168],"smooth":[118],"case.":[119],"We":[120],"integrate":[121],"quadratic":[124],"order":[125],"sphere":[129],"projection":[130],"learning":[132],"latent":[134],"dynamics":[135],"efficiently":[136],"while":[137],"preserving":[138],"stability.":[139],"Numerical":[140],"experiments":[141],"demonstrate":[142,177],"that":[143],"our":[144],"full":[145],"model":[146],"outperforms":[147],"ROM":[148],"methods":[150],"such":[151],"as":[152,183],"Extended":[153],"Dynamic":[154,159],"Mode":[155,160],"Decomposition,":[156],"Bagging":[157],"Optimised":[158],"Decomposition":[161],"Linear":[163],"Nonlinear":[165],"Disambiguation":[166],"Optimisation":[167],"terms":[169],"accuracy":[171],"or":[172],"computational":[173],"costs.":[174],"These":[175],"results":[176],"potential":[179],"robust":[185],"stable":[187],"tool":[188]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-13T00:00:00"}