Multilevel ensemble Kalman filtering for spatio-temporal processes

Numerische Mathematik, vol. 147, pp. 71–125

Abstract

Abstract We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We consider underlying models that needs to be simulated by numerical methods, with discretization in both space and time. The multilevel Monte Carlo sampling strategy, achieving variance reduction through pairwise coupling of ensemble particles on neighboring resolutions, is used in the sample-moment step of MLEnKF to produce an efficent hierarchical filtering method for spatio-temporal models. Under sufficent regularity, MLEnKF is proven to be more efficient for weak approximations than EnKF, asymptotically in the large-ensemble and fine-numerical-resolution limit. Numerical examples support our theoretical findings.

Authors 5

1. Alexey Chernov

   Carl von Ossietzky Universität Oldenburg

   Affiliation as printed

   Institute for Mathematics, Carl von Ossietzky University Oldenburg, Oldenburg, Germany

   Univ. of Oldenburg

2. Håkon Hoel Aachen Chair of Mathematics for Uncertainty Quantification

   RWTH Aachen University

   Affiliation as printed

   Chair of Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany

   RWTH Aachen University

3. Kody J. H. Law corresponding

   University of Manchester

   Affiliation as printed

   Department of Mathematics, University of Manchester, Manchester, UK

   University of Manchester

4. Fabio Nobile

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   Institute of Mathematics, École polytechnique fédérale de Lausanne, Lausanne, Switzerland

   École Polytechnique Fédérale de Lausanne,

5. Raul F. Tempone Aachen Chair of Mathematics for Uncertainty Quantification

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia

   Chair of Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany

   RWTH Aachen University