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Presenter: Paul Krause

Seminar Title: The Diffusion Kernal Filter

The available nonlinear methods for solving the discrete-time Filtering problem, in Data Assimilation, suffer from two major drawbacks: large operations count and troubles defining prediction. The Diffusion Kernel Filter is a sample-based method for Itô SDEs arrived at by a parametrization of small fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The established parametrization of fluctuations is a dual-formula for the linear analysis of sensitivity to initial perturbations and the short-time analysis of sensitivity to Brownian perturbations in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Results for Lorenz-63 will be presented and the future avenues with moderate dimensions discussed.

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