In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient filtering method called multi-index EnKF (MIEnKF). MIEnKF is based on independent samples of four-coupled EnKF estimators on a multi-index hierarchy of resolution levels, and it may be viewed as an extension of the multilevel EnKF (MLEnKF) method developed by the same authors in 2020. Multi-index here refers to a two-index method, consisting of a hierarchy of EnKF estimators that are coupled in two degrees of freedom: time discretization and ensemble size. Under certain assumptions, when strong coupling between solutions on neighboring numerical resolutions is attainable, the MIEnKF method is proven to be more tractable than EnKF and MLEnKF. Said efficiency gains are also verified numerically in a series of test problems.
Bibliographical noteKAUST Repository Item: Exported on 2022-09-09
Acknowledged KAUST grant number(s): URF/1/2584-01-01
Acknowledgements: This work was supported by the KAUST Office of Sponsored Research (OSR) under Award No. URF/1/2584-01-01 and the Alexander von Humboldt Foundation. G. Shaimerdenova and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications