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

TittelBayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization
PublikasjonstypeJournal Article
Utgivelseår2020
ForfattereBocquet, M, Brajard, J, Carrassi, A, Bertino, L
TidsskriftFoundations of Data Science
Volum2
ISSN2158-2491
Sammendrag

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.

DOI10.3934/fods.2020004
Refereed DesignationRefereed
Forfatterens adresse

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