{"title":"Modelling View on Numerical Uncertainty Quantification for Dynamical Systems","authors":"Dirk Langemann , Katja Tüting","doi":"10.1016/j.ifacol.2025.03.055","DOIUrl":null,"url":null,"abstract":"<div><div>We present a modelling view on the numerical quantification of uncertainties in the solution of a dynamical system, which mostly consists in using a linearized update procedure for the covariance matrix. We regard the Fokker-Planck equation for the probability density of the states of the dynamical system as ground truth and the numerical method as surrogate model. We give an error estimate and show the connection to the numerical solution of ordinary differential equations. Finally, uncertainty quantification is interpreted as measurement.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"59 1","pages":"Pages 319-324"},"PeriodicalIF":0.0000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IFAC-PapersOnLine","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2405896325002721","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/27 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We present a modelling view on the numerical quantification of uncertainties in the solution of a dynamical system, which mostly consists in using a linearized update procedure for the covariance matrix. We regard the Fokker-Planck equation for the probability density of the states of the dynamical system as ground truth and the numerical method as surrogate model. We give an error estimate and show the connection to the numerical solution of ordinary differential equations. Finally, uncertainty quantification is interpreted as measurement.
期刊介绍：
All papers from IFAC meetings are published, in partnership with Elsevier, the IFAC Publisher, in theIFAC-PapersOnLine proceedings series hosted at the ScienceDirect web service. This series includes papers previously published in the IFAC website.The main features of the IFAC-PapersOnLine series are: -Online archive including papers from IFAC Symposia, Congresses, Conferences, and most Workshops. -All papers accepted at the meeting are published in PDF format - searchable and citable. -All papers published on the web site can be cited using the IFAC PapersOnLine ISSN and the individual paper DOI (Digital Object Identifier). The site is Open Access in nature - no charge is made to individuals for reading or downloading. Copyright of all papers belongs to IFAC and must be referenced if derivative journal papers are produced from the conference papers. All papers published in IFAC-PapersOnLine have undergone a peer review selection process according to the IFAC rules.
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