Articles | Volume 30, issue 2
Research article
09 Jun 2023
Research article |  | 09 Jun 2023

Data-driven reconstruction of partially observed dynamical systems

Pierre Tandeo, Pierre Ailliot, and Florian Sévellec

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Cited articles

Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models, Nonlin. Processes Geophys., 26, 143–162,, 2019. a
Brajard, J., Carrassi, A., Bocquet, M., and Bertino, L.: Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: A case study with the Lorenz 96 model, Journal of Computational Science, 44, 101171,, 2020. a
Brajard, J., Carrassi, A., Bocquet, M., and Bertino, L.: Combining data assimilation and machine learning to infer unresolved scale parametrization, Philos. T. Roy. Soc. A, 379, 2194,, 2021. a
Brunton, S. L., Proctor, J. L., and Kutz, J. N.: Discovering governing equations from data by sparse identification of nonlinear dynamical systems, P. Natl. Acad. Sci. USA, 113, 3932–3937, 2016. a
Brunton, S. L., Brunton, B. W., Proctor, J. L., Kaiser, E., and Kutz, J. N.: Chaos as an intermittently forced linear system, Nat. Commun., 8, 19,, 2017. a
Short summary
The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system without knowing the model equations. It is illustrated using the three-dimensional Lorenz system, where only two components are observed. The proposed data-driven procedure is low-cost, is easy to implement, uses linear and Gaussian assumptions and requires only a small amount of data. It is based on an iterative linear Kalman smoother with a state augmentation.