29 Nov 2022
29 Nov 2022
Status: this preprint is open for discussion.

Data-driven Reconstruction of Partially Observed Dynamical Systems

Pierre Tandeo1,2,3, Pierre Ailliot4, and Florian Sévellec5 Pierre Tandeo et al.
  • 1IMT Atlantique, Lab-STICC, UMR CNRS 6285, F-29238, France
  • 2Odyssey, Inria/IMT, France
  • 3RIKEN Center for Computational Science, Kobe, 650-0047, Japan
  • 4Univ Brest, UMR CNRS 6205, Laboratoire de Mathematiques de Bretagne Atlantique, France
  • 5Laboratoire d’Océanographie Physique et Spatiale, Univ Brest CNRS IRD Ifremer, Brest, France

Abstract. The state of the atmosphere, or of the ocean, cannot be exhaustively observed. Crucial parts might remain out of reach of proper monitoring. Also, defining the exact set of equations driving the atmosphere and ocean is virtually impossible because of their complexity. Hence, the goal of this paper is to obtain predictions of a partially observed dynamical system, without knowing the model equations. In this data-driven context, the article focuses on the Lorenz-63 system, where only the second and third components are observed, and access to the equations is not allowed. To account to those strong constraints, a combination of machine learning and data assimilation techniques is proposed. The key aspects are the following: the introduction of latent variables, a linear approximation of the dynamics, and a database that is updated iteratively, maximising the innovation likelihood. We find that the latent variables inferred by the procedure are related to the successive derivatives of the observed components of the dynamical system. The method is also able to reconstruct accurately the local dynamics of the partially observed system. Overall, the proposed methodology is simple, easy to code, and gives promising results, even in the case of small amounts of observations.

Pierre Tandeo et al.

Status: open (extended)

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Pierre Tandeo et al.

Pierre Tandeo et al.


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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 3-dimensional Lorenz system where only two components are observed. In the era of deep learning and large datasets, the proposed data-driven procedure is low-cost, easy to implement, using linear and Gaussian assumptions, and requires only a small amount of data.