TY - JOUR
T1 - Multi-index Ensemble Kalman Filtering
AU - Hoel, Hakon
AU - Shaimerdenova, Gaukhar
AU - Tempone, Raul
N1 - KAUST 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.
PY - 2022/8/30
Y1 - 2022/8/30
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/680994
UR - https://www.sciencedirect.com/science/article/pii/S0021999122006234
U2 - 10.1016/j.jcp.2022.111561
DO - 10.1016/j.jcp.2022.111561
M3 - Article
SN - 0021-9991
SP - 111561
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -