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A model-data weak formulation for simultaneous estimation of state and model bias

Author(s)
Yano, Masayuki; Penn, James Douglass; Patera, Anthony T.
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Alternative title
A model-data weak formulation for simultaneous estimation of state and model bias Estimation de la variable dʼétat et du biais de modèle par une formulation faible incorporant les données
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Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/
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Abstract
We introduce a Petrov–Galerkin regularized saddle approximation which incorporates a “model” (partial differential equation) and “data” (M experimental observations) to yield estimates for both state and model bias. We provide an a priori theory that identifies two distinct contributions to the reduction in the error in state as a function of the number of observations, M: the stability constant increases with M; the model-bias best-fit error decreases with M. We present results for a synthetic Helmholtz problem and an actual acoustics system.
Date issued
2013-11
URI
http://hdl.handle.net/1721.1/103882
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Comptes Rendus Mathematique
Publisher
Elsevier
Citation
Yano, Masayuki, James D. Penn, and Anthony T. Patera. “A Model-Data Weak Formulation for Simultaneous Estimation of State and Model Bias.” Comptes Rendus Mathematique 351, no. 23–24 (December 2013): 937–941.
Version: Original manuscript
ISSN
1631073X

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