Manuscript accepted by Journal of Computational Physics
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The manuscript entitled "Multi-index ensemble Kalman filtering" by Prof. Raul Tempone, Gaukhar Shaimerdenova, and Håkon A. Hoel has been accepted by the Journal of Computational Physics (JCP).The JCP is a bimonthly scientific journal covering original scientific contributions in advanced mathematical and numerical modeling reflecting a combination of concepts, methods, and principles of physics, mechanics, applied mathematics, statistics, applied geometry, computer science, chemistry, and other scientific disciplines as well. It was established in 1966 and is published by Elsevier. According to the Journal Citation Reports, the impact factor of the JCP is 4.645, ranking it 3 out of 56 in the category of Physics, Mathematical.
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.