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DOI	10.1073/pnas.2015006118
	Statistical finite elements for misspecified models
	Duffin C.; Cripps E.; Stemler T.; Girolami M.
发表日期	2021
ISSN	00278424
卷号	118 期号:2
英文摘要	We present a statistical finite element method for nonlinear, time-dependent phenomena, illustrated in the context of nonlinear internal waves (solitons). We take a Bayesian approach and leverage the finite element method to cast the statistical problem as a nonlinear Gaussian state-space model, updating the solution, in receipt of data, in a filtering framework. The method is applicable to problems across science and engineering for which finite element methods are appropriate. The Korteweg-de Vries equation for solitons is presented because it reflects the necessary complexity while being suitably familiar and succinct for pedagogical purposes. We present two algorithms to implement this method, based on the extended and ensemble Kalman filters, and demonstrate effectiveness with a simulation study and a case study with experimental data. The generality of our approach is demonstrated in SI Appendix, where we present examples from additional nonlinear, time-dependent partial differential equations (Burgers equation, Kuramoto-Sivashinsky equation). © This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY).
英文关键词	Bayesian calibration; Finite element methods; Model discrepancy
语种	英语
来源期刊	Proceedings of the National Academy of Sciences of the United States of America
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/181048
作者单位	Department of Mathematics and Statistics, University of Western Australia, Perth, WA 6009, Australia; Complex Systems Group, University of Western Australia, Perth, WA 6009, Australia; Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, United Kingdom; Lloyd's Register Foundation Programme for Data-Centric Engineering, Alan Turing Institute, London, NW1 2DB, United Kingdom
推荐引用方式 GB/T 7714	Duffin C.,Cripps E.,Stemler T.,et al. Statistical finite elements for misspecified models[J],2021,118(2).
APA	Duffin C.,Cripps E.,Stemler T.,&Girolami M..(2021).Statistical finite elements for misspecified models.Proceedings of the National Academy of Sciences of the United States of America,118(2).
MLA	Duffin C.,et al."Statistical finite elements for misspecified models".Proceedings of the National Academy of Sciences of the United States of America 118.2(2021).