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Ensemble forecasts in reproducing kernel Hilbert space family: dynamical systems in Wonderland

Berenger Hug 1, 2 Etienne Mémin 1, 3, 2 Gilles Tissot 1, 2 
1 ODYSSEY - Océan Dynamique Observations Analyse
UBO UFR ST - Université de Bretagne Occidentale - UFR Sciences et Techniques, UR1 - Université de Rennes 1, IFREMER - Institut Français de Recherche pour l'Exploitation de la Mer, Inria Rennes – Bretagne Atlantique , IMT Atlantique - IMT Atlantique
Abstract : A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing kernel Hilbert spaces with kernel functions driven by the dynamics. This family is nicknamed Wonderland for its appealing properties. In Wonderland the Koopman and Perron-Frobenius operators are unitary and uniformly continuous. This property warrants they can be expressed in exponential series of diagonalizable bounded infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. Wonderland enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constant-in-time linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems.
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Submitted on : Saturday, July 30, 2022 - 1:05:42 PM
Last modification on : Friday, August 5, 2022 - 2:54:52 PM


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  • HAL Id : hal-03740500, version 1


Berenger Hug, Etienne Mémin, Gilles Tissot. Ensemble forecasts in reproducing kernel Hilbert space family: dynamical systems in Wonderland. 2022. ⟨hal-03740500⟩



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