Homogenized Hybrid Particle Filters in Multi-scale Environments
Seminar Room 1, Newton Institute
Multi-scale problems are commonly recognized for their complexity, yet the main challenge in multi-scale modeling is to recognize their simplicity, and make use of it to see how information interacts with these complex structures and scales. This paper outlines efficient methods that combine the information from the observations with the dynamics of coupled ocean - atmosphere models and seeks to improve decadal climate predictions by developing, testing, and improving the initialization of different components of the Earth system, particularly the ocean.
We present a reduced-order particle filtering algorithm, the Homogenized Hybrid Particle Filter (HHPF), for state estimation in nonlinear multi-scale dynamical systems. This method combines stochastic homogenization with nonlinear filtering theory to construct an efficient particle filtering algorithm for the approximation of a reduced-order nonlinear filter for multi-scale systems. In this work, we show that the HHPF gives a good approximation of the conditional law of the coarse-grained dynamics in the limit as the scaling parameter goes to zero and the number of particles is sufficiently large.