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

Bocquet, M., Brajard, J., Carrassi, A. ORCID: https://orcid.org/0000-0003-0722-5600 and Bertino, L. (2020) Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization. Foundations of Data Science, 2 (1). pp. 55-80. ISSN 2639-8001 doi: 10.3934/fods.2020004

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/89798
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Institute of Mathematical Sciences
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