Séminaire
In physical applications, dynamical models and observational data play dual roles in prediction and uncertainty quantification, each representing sources of incomplete and inaccurate information. In data rich problems, first-principle physical laws constrain the degrees of freedom of massive data sets, utilizing our prior insights to complex processes. Respectively, in data sparse problems, dynamical models fill spatial and temporal gaps in observational networks. The dynamical chaos characteristic of these process models is, however, among the primary sources of forecast uncertainty in complex physical systems. Observations are thus required to update predictions where there is sensitivity to initial conditions and uncertainty in model parameters. Broadly referred to as data assimilation, or stochastic filtering, the techniques used to combine these disparate sources of information include methods from Bayesian inference, dynamical systems and optimal control. While the butterfly effect renders the forecasting problem inherently volatile, chaotic dynamics also put strong constraints on the evolution of errors. It is well understood in the weather prediction community that the growth of forecast uncertainty is confined to a much lower dimensional subspace corresponding to the directions of rapidly growing perturbations. The Assimilation in the Unstable Subspace (AUS) methodology of Trevisan et al. has offered understanding of the mechanisms governing the evolution of uncertainty in ensemble forecasting, exploiting this dimensional reduction prescribed by the dynamics. With my collaborators, I am studying the mathematical foundations of ensemble based filtering in the perspective of smooth and random dynamical systems.
bruno.deremble@ens.fr