{"id":"https://openalex.org/W4387540966","doi":"https://doi.org/10.1038/s41586-023-06574-8","title":"State estimation of a physical system with unknown governing equations","display_name":"State estimation of a physical system with unknown governing equations","publication_year":2023,"publication_date":"2023-10-11","ids":{"openalex":"https://openalex.org/W4387540966","doi":"https://doi.org/10.1038/s41586-023-06574-8","pmid":"https://pubmed.ncbi.nlm.nih.gov/37821594"},"language":"en","primary_location":{"id":"doi:10.1038/s41586-023-06574-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-023-06574-8","pdf_url":"https://www.nature.com/articles/s41586-023-06574-8.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.nature.com/articles/s41586-023-06574-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088673192","display_name":"Kevin Course","orcid":"https://orcid.org/0009-0008-8813-2441"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Kevin Course","raw_affiliation_strings":["Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada"],"raw_orcid":"https://orcid.org/0009-0008-8813-2441","affiliations":[{"raw_affiliation_string":"Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075671693","display_name":"Prasanth B. Nair","orcid":"https://orcid.org/0000-0001-7371-1223"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I2799838188","display_name":"Toronto Rehabilitation Institute","ror":"https://ror.org/00mxe0976","country_code":"CA","type":"healthcare","lineage":["https://openalex.org/I1325899441","https://openalex.org/I2799838188"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Prasanth B. Nair","raw_affiliation_strings":["Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada. prasanth.nair@utoronto.ca","Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada. prasanth.nair@utoronto.ca","institution_ids":["https://openalex.org/I2799838188"]},{"raw_affiliation_string":"Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088673192"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":9750,"currency":"EUR","value_usd":11690},"apc_paid":{"value":9750,"currency":"EUR","value_usd":11690},"fwci":8.615,"has_fulltext":true,"cited_by_count":53,"citation_normalized_percentile":{"value":0.98339793,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"622","issue":"7982","first_page":"261","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9927999973297119,"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/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5904086232185364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5722636580467224},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5089375972747803},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.48865750432014465},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.4577999413013458},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.43931931257247925},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4236999750137329},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.4109760522842407},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4061264097690582},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3538759648799896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34926003217697144},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31707099080085754},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25282806158065796}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5904086232185364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5722636580467224},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5089375972747803},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.48865750432014465},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.4577999413013458},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.43931931257247925},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4236999750137329},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.4109760522842407},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4061264097690582},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3538759648799896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34926003217697144},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31707099080085754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25282806158065796},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1038/s41586-023-06574-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-023-06574-8","pdf_url":"https://www.nature.com/articles/s41586-023-06574-8.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},{"id":"pmid:37821594","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37821594","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10567554","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10567554","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10567554/pdf/41586_2023_Article_6574.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Nature","raw_type":"Text"},{"id":"pmh:oai:RePEc:nat:nature:v:622:y:2023:i:7982:d:10.1038_s41586-023-06574-8","is_oa":false,"landing_page_url":"https://www.nature.com/articles/s41586-023-06574-8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"doi:10.1038/s41586-023-06574-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41586-023-06574-8","pdf_url":"https://www.nature.com/articles/s41586-023-06574-8.pdf","source":{"id":"https://openalex.org/S137773608","display_name":"Nature","issn_l":"0028-0836","issn":["0028-0836","1476-4687"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nature","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387540966.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1587348082","https://openalex.org/W1928379838","https://openalex.org/W1978060721","https://openalex.org/W1980586072","https://openalex.org/W2020934227","https://openalex.org/W2047425707","https://openalex.org/W2083402998","https://openalex.org/W2088748973","https://openalex.org/W2105934661","https://openalex.org/W2112823474","https://openalex.org/W2121593555","https://openalex.org/W2127465530","https://openalex.org/W2137258853","https://openalex.org/W2153155589","https://openalex.org/W2157969058","https://openalex.org/W2239232218","https://openalex.org/W2295695367","https://openalex.org/W2332182247","https://openalex.org/W2332297685","https://openalex.org/W2469805270","https://openalex.org/W2745007981","https://openalex.org/W2757438722","https://openalex.org/W2797828728","https://openalex.org/W2963816767","https://openalex.org/W2964145209","https://openalex.org/W2970971581","https://openalex.org/W3028073062","https://openalex.org/W3045993716","https://openalex.org/W3086458503","https://openalex.org/W3167053542","https://openalex.org/W3197500030","https://openalex.org/W3200208184","https://openalex.org/W3201490607","https://openalex.org/W3211856448","https://openalex.org/W3212326852","https://openalex.org/W3215447930","https://openalex.org/W4211049957","https://openalex.org/W4211127940","https://openalex.org/W4231204432","https://openalex.org/W4307291022","https://openalex.org/W4383097042","https://openalex.org/W6630233047","https://openalex.org/W6968637484"],"related_works":["https://openalex.org/W2372267530","https://openalex.org/W4303857162","https://openalex.org/W1919985504","https://openalex.org/W2965643117","https://openalex.org/W3015855446","https://openalex.org/W4288266653","https://openalex.org/W2407375987","https://openalex.org/W2032094637","https://openalex.org/W2950975704","https://openalex.org/W2010643158"],"abstract_inverted_index":{"Abstract":[0],"State":[1],"estimation":[2,88],"is":[3,60],"concerned":[4],"with":[5,13,76],"reconciling":[6],"noisy":[7],"observations":[8],"of":[9,25,45,136,171],"a":[10,69,122,168],"physical":[11],"system":[12,96],"the":[14,23,43,91,95,114,118,134,157],"mathematical":[15,48,119],"model":[16,120],"believed":[17],"to":[18,107,139,146,159,167],"predict":[19],"its":[20],"behaviour":[21],"for":[22,72,86],"purpose":[24],"inferring":[26],"unmeasurable":[27],"states":[28],"and":[29,121],"denoising":[30],"measurable":[31],"ones":[32],"1,2":[33],".":[34,65],"Traditional":[35],"state-estimation":[36,109,137],"techniques":[37],"rely":[38],"on":[39,154],"strong":[40],"assumptions":[41],"about":[42],"form":[44],"uncertainty":[46],"in":[47,62,89,117,173],"models,":[49],"typically":[50],"that":[51,80,141],"it":[52],"manifests":[53],"as":[54],"an":[55,82,127],"additive":[56],"stochastic":[57,73,160],"perturbation":[58],"or":[59,102],"parametric":[61],"nature":[63],"3":[64],"Here":[66],"we":[67,152],"present":[68],"reparametrization":[70],"trick":[71],"variational":[74,161],"inference":[75,162],"Markov":[77],"Gaussian":[78],"processes":[79],"enables":[81,133],"approximate":[83,128],"Bayesian":[84,129],"approach":[85],"state":[87,123,155],"which":[90],"equations":[92],"governing":[93],"how":[94],"evolves":[97],"over":[98],"time":[99],"are":[100,165],"partially":[101],"completely":[103],"unknown.":[104],"In":[105],"contrast":[106],"classical":[108],"techniques,":[110],"our":[111],"method":[112],"learns":[113],"missing":[115],"terms":[116],"estimate":[124],"simultaneously":[125],"from":[126],"perspective.":[130],"This":[131],"development":[132],"application":[135],"methods":[138],"problems":[140,172],"have":[142],"so":[143],"far":[144],"proved":[145],"be":[147],"beyond":[148],"reach.":[149],"Finally,":[150],"although":[151],"focus":[153],"estimation,":[156],"advancements":[158],"made":[163],"here":[164],"applicable":[166],"broader":[169],"class":[170],"machine":[174],"learning.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":23},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}