Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization

• URL: http://arxiv.org/abs/2001.06270v2
• Date: Fri, 27 Mar 2020 19:52:25 GMT
• Title: Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization
• Authors: Marc Bocquet, Julien Brajard, Alberto Carrassi, Laurent Bertino
• Abstract summary: We show how to combine data assimilation and machine learning in several ways to reconstruct high-dimensional chaotic dynamics. We numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

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