Comptes Rendus
no. 23-24
Numerical analysis
A model-data weak formulation for simultaneous estimation of state and model bias

Presented by: Olivier Pironneau

Masayuki Yano1; James D. Penn1; Anthony T. Patera1
1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.034

Masayuki Yano 1; James D. Penn 1; Anthony T. Patera 1

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 
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Masayuki Yano; James D. Penn; Anthony T. Patera. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.034/

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