H.B. Keller Colloquium

Ensemble Kalman filters constitute a methodology for incorporating noisy data into complex dynamical models to enhance predictive capability. They are widely adopted in the geophysical sciences, underpinning weather forecasting for example, and are starting to be used throughout the sciences and engineering; furthermore, they have been adapted to function as a general-purpose tool for parametric inference. The strength of these methods stems from their ability to operate using complex models as a black box, together with their natural adaptation to high performance computers. In this work we provide, for the first time, theory to elucidate conditions under which this widely adopted methodology provides accurate model predictions and uncertainties. The theory rests on a mean-field formulation of the methodology and an error analysis controlling differences between probability measure propagation under the mean-field model and under the true filtering distribution.

The mean-field formulation is based on joint work with Edoardo Calvello (Caltech) and Sebastian Reich (Potsdam). The error analysis is based on joint work with Jose Carrillo (Oxford), Franca Hoffmann (Caltech) and Urbain Vaes (Paris).