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

2024/12/18 by Daniel Sanz-Alonso, Sanz-Alonso, Daniel, Nathan Waniorek +1 · 2 citations
Computer Science · #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2412.14318

Abstract

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.

Cited by

• Filtering with Randomised Observations: Sequential Learning of Relevant Subspace Properties and Accuracy Analysis
• Error analysis of the projected PO method with additive inflation for the partially observed Lorenz 96 model

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