Ensemble Forecasts in Reproducing Kernel Hilbert Space Manifold : Dynamical Systems in Wonderland
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 manifold of reproducible kernel Hilbert spaces with kernel functions driven by the dynamics. This manifold is nicknamed Wonderland for its appealing properties. In Wonderland the Koopman and Perron-Frobenius operator are unitary and uniformly continuous. They can be safely 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
Year of publication: |
[2022]
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Authors: | Memin, Etienne ; Hug, Berenger ; Tissot, Gilles |
Publisher: |
[S.l.] : SSRN |
Subject: | Prognoseverfahren | Forecasting model | Schätztheorie | Estimation theory | Prognose | Forecast |
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