Numerical analysis
A model-data weak formulation for simultaneous estimation of state and model bias
Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 937-941.

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.

Nous présentons une approximation de Petrov–Galerkin pour un problème de point selle incorporant un « modèle » (équation aux dérivées partielles) et des « données » (M observations expérimentales) afin dʼobtenir une estimation conjointe de la variable dʼétat et du biais de modèle. Notre théorie a priori identifie deux contributions à la décroissance de lʼerreur sur lʼétat en fonction du nombre dʼobservations expérimentales, M : la croissance de la constante stabilité avec M ; la décroissance de lʼestimation par moindre carré du biais de modèle avec M. Nous présentons des résultats pour un problème de Helmholtz synthétique ainsi que pour un système acoustique réel.

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DOI: 10.1016/j.crma.2013.10.034
Yano, Masayuki 1; Penn, James D. 1; Patera, Anthony T. 1

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Yano, Masayuki; Penn, James D.; Patera, Anthony T. A model-data weak formulation for simultaneous estimation of state and model bias. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 937-941. doi : 10.1016/j.crma.2013.10.034. http://www.numdam.org/articles/10.1016/j.crma.2013.10.034/

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