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

Autor:	Sanz-Alonso, Daniel, Waniorek, Nathan
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Numerical Analysis Statistics - Machine Learning 62F15 68Q25 60G35 62M05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 40 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.14318 Zobrazit plný text záznamu View this record from Arxiv