Online learning of both state and dynamics using ensemble Kalman filters

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.

arXiv comment26 pages, 7 figures

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• Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation
• Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation
• Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components
• State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics
• Development of an offline and online hybrid model for the Integrated Forecasting System
• Inferring the instability of a dynamical system from the skill of data assimilation exercises