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Ensemble transform filters for data assimilation

le 12 octobre 2011

14H - Groupe de travail "Applications des Mathématiques"

ENS Rennes Bâtiment Sauvy, Salle 5 (rdc)

Séminaire de Sebastian Reich (Université de Potsdam, Allemagne) au groupe de travail "Applications des mathématiques"

Lien vers la page Web de l'orateur Résumé : Data assimilation is the task to combine model based simulations with measurements to provide optimal state and/or parameter estimates. Data assimilation requires that one can quantify the uncertainty in the mathematical model forecasts. Bayes' theorem is used to assimilate observations into the model forecast and to reduce uncertainties. I will discuss the data assimilation filtering problem in the context of a McKean-Vlasov system for the time evolution of the probability density function characterizing model uncertainty. Specific algorithms are obtained by using ensemble/particle methods for the time evolution of the probability density functions under the model dynamics and by fitting statistical models to the ensemble of particles such as Gaussians and Gaussian mixture models prior to a data assimilation step. Contrary to particle filters (or sequential Monte Carlo methods, the data assimilation step itself is implemented as a transport of the ensemble/particles under continuous transformations. The resulting filters can be viewed as generalizations of the popular ensemble Kalman filter to non-Gaussian probability density functions.

Recherche - Valorisation
Erwan Faou et Yannick Privat

Mise à jour le 29 septembre 2011