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Session I.6 - Mathematical Foundations of Data Assimilation and Inverse Problems

Wednesday, June 14, 15:30 ~ 16:00

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Daniel Sanz-Alonso

University of Chicago, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. In this talk I will introduce a non-asymptotic analysis of ensemble Kalman updates that rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. I will present the theory in a unified framework, comparing several implementations of ensemble Kalman updates that use perturbed observations, square root filtering, and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Joint work with Omar Al Ghattas (University of Chicago).

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