Single-ensemble multilevel Monte Carlo for discrete ensemble Kalman methods

Abstract: Ensemble Kalman methods solve problems in domains such as filtering and inverse problems with interacting particles that evolve over time. For computationally expensive problems, the cost of attaining a high accuracy quickly becomes prohibitive. We exploit a hierarchy of approximations to the underlying forward model and apply multilevel Monte Carlo (MLMC) techniques, improving the asymptotic cost-to-error relation. More specifically, we use MLMC at each time step to estimate the interaction term in a single, globally-coupled ensemble. This technique was proposed by Hoel et al. for the ensemble Kalman filter; our goal is to study its applicability to a broader family of ensemble Kalman methods.