CUED Publications database

Statistical finite elements for misspecified models

Duffin, C and Cripps, E and Stemler, T and Girolami, M (2021) Statistical finite elements for misspecified models. Proceedings of the National Academy of Sciences of the United States of America, 118. ISSN 0027-8424

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Abstract

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).

Item Type: Article
Uncontrolled Keywords: Bayesian calibration finite element methods model discrepancy
Subjects: UNSPECIFIED
Divisions: UNSPECIFIED
Depositing User: Cron Job
Date Deposited: 30 Dec 2020 21:23
Last Modified: 13 Apr 2021 07:03
DOI: 10.1073/pnas.2015006118