Online learning of both state and dynamics using ensemble Kalman filters

TL;DR

This paper explores online learning of system states and dynamics using ensemble Kalman filters, enabling real-time updates with new observations in chaotic Lorenz models.

Contribution

It introduces and compares global, local, and iterative EnKF methods for online learning of both states and dynamics in chaotic systems.

Findings

EnKF methods effectively learn system dynamics online.

Local EnKF improves computational efficiency.

All methods demonstrate good accuracy on Lorenz models.

Abstract

The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning representations of the surrogate model can be used within a Bayesian data assimilation framework. However, these approaches require to consider long time series of observational data, meant to be assimilated all together. This paper investigates the possibility to learn both the dynamics and the state online, i.e. to update their estimates at any time, in particular when new observations are acquired. The estimation is based on the ensemble Kalman filter (EnKF) family of algorithms using a rather simple representation for the surrogate model and state augmentation. We consider the implication of learning dynamics online through (i) a global EnKF, (i) a local EnKF and (iii) an iterative EnKF and we discuss in each case issues and algorithmic solutions. We then demonstrate numerically the efficiency and assess the accuracy of these methods using one-dimensional, one-scale and two-scale chaotic Lorenz models.