Multilevel ensemble Kalman filtering for spatially extended models

Abstract

The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of the classical Monte Carlo method, which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this talk I will present ideas on combining MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite and infinite dimensional state spaces. Theoretical results and numerical studies of the performance gain of MLEnKF over EnKF will also be presented.

(Joint work with Alexey Chernov, Kody J. H. Law, Fabio Nobile, and Raul Tempone.)