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

TL;DR

This paper proves that ensemble Kalman filters can maintain accurate state estimates over long periods for complex chaotic systems, including those modeled by machine learning, under certain conditions.

Contribution

It provides theoretical guarantees for the long-time accuracy of ensemble Kalman filters in high-dimensional, chaotic, and machine-learned dynamical systems.

Findings

Establishes conditions for long-term accuracy of ensemble Kalman filters.

Validates the use of machine-learned models in data assimilation.

Applies theory to Navier-Stokes and Lorenz systems.

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.