Abstract
Multifidelity methods aim to leverage the availability of models at different levels of fidelity describing the same physical phenomena and are receiving growing attention in computational science. One field that can considerably benefits from statistical multifidelity approaches is data assimilation. This chapter presents a broad overview of multifidelity methods in data assimilation for hierarchies of models and hierarchies of observations. We introduce the theoretical multifidelity Kalman filter, and discuss its practical implementation using an ensemble-based framework as the multifidelity ensemble Kalman filter (MFEnKF). The discussion builds upon the theory of linear and nonlinear control variates. Numerical examples compare the multifidelity and the traditional EnKF.
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Acknowledgements
The authors would like to acknowledge Traian Iliescu and Changhong Mou who have helped make some of the work underlying this possible. This work was supported by awards NSF CCF–1613905. NSF ACI–1709727, NSF CDS&E-MSS–1953113, and by the Computational Science Laboratory at Virginia Tech.
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Popov, A.A., Sandu, A. (2022). Multifidelity Data Assimilation for Physical Systems. In: Park, S.K., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. IV). Springer, Cham. https://doi.org/10.1007/978-3-030-77722-7_2
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DOI: https://doi.org/10.1007/978-3-030-77722-7_2
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