Sumati Surya (Raman Research Institute, Bangalore, India)
Alessio Spantini (Massachusetts Institute of Technology, USA)
We introduce a class of structure-exploiting nonlinear filters for high-dimensional state-space models with intractable transition kernels. The idea is to transform the forecast ensemble into samples from the current filtering distribution by means of a sequence of local (in state-space) nonlinear couplings computed mostly via low-dimensional convex optimization. This sequence of low-dimensional transformations implicitly approximates the projection of the filtering distribution onto a manifold of sparse Markov random fields (not necessarily Gaussian) and can be carried out with limited ensemble sizes. Many square-root ensemble Kalman filters can be interpreted as special instances of the proposed framework when we restrict our attention exclusively to linear transformations, and when we neglect approximately sparse Markov structure in the filtering distribution. We consider applications to chaotic dynamical systems. This is joint work with Prof. Youssef Marzouk.