Single-ensemble multilevel Monte Carlo for discrete ensemble Kalman methods

TL;DR

This paper introduces a multilevel Monte Carlo approach to improve the efficiency of ensemble Kalman methods in computationally expensive filtering and inverse problems, extending previous work to a broader class of methods.

Contribution

It applies multilevel Monte Carlo techniques at each time step to enhance the computational efficiency of ensemble Kalman methods beyond the filter.

Findings

Improved asymptotic cost-to-error relation for ensemble Kalman methods.

Demonstrated applicability of MLMC to a broader family of ensemble Kalman algorithms.

Potential reduction in computational cost for high-accuracy solutions.

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.