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

Bocquet, M., Brajard, J., Carrassi, A. 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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:89798
Publisher:American Institute of Mathematical Sciences

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