mlsanityData to 14 Oct 2026

Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems

arXiv 2412.14318 ↗First posted 18 Dec 2024math.DS cs.NA math.NAcited by 1

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Abstract (arXiv)

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper establishes long-time accuracy of ensemble Kalman filters. We introduce conditions on the dynamics and the observations under which the estimation error remains small in the long-time horizon. Our theory covers a wide class of partially-observed chaotic dynamical systems, which includes the Navier-Stokes equations and Lorenz models. In addition, we prove long-time accuracy of ensemble Kalman filters with surrogate dynamics, thus validating the use of machine-learned forecast models in ensemble data assimilation.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 32 of its 77 references that are in the map. First posted on arXiv 18 Dec 2024.

Builds on

32 of 77 references.

References · 32

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20 more
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  1. 2025Filtering with Randomised Observations: Sequential Learning of Relevant Subspace Properties and Accuracy Analysiscited by 0