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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 28 Feb 2019

Research article | 28 Feb 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Data assimilation as a deep learning tool to infer ODE representations of dynamical models

Marc Bocquet1, Julien Brajard2,3, Alberto Carrassi3,4, and Laurent Bertino3 Marc Bocquet et al.
  • 1CEREA, joint laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, France
  • 2Sorbonne University, CNRS-IRD-MNHN, LOCEAN, Paris, France
  • 3Nansen Environmental and Remote Sensing Center, Bergen, Norway
  • 4Geophysical Institute, University of Bergen, Norway

Abstract. Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from its output, resorting in particular to neural networks and deep learning techniques. We will show how the same goal can be directly achieved using data assimilation techniques without leveraging on machine learning software libraries, with a view to high-dimensional models. The dynamics of a model are learned from its observation and an ordinary differential equation (ODE) representation of this model is inferred using a recursive nonlinear regression. Because the method is embedded in a Bayesian data assimilation framework, it can learn from partial and noisy observations of a state trajectory of the physical model. Moreover, a space-wise local representation of the ODE system is introduced and is key to cope with high-dimensional models.

It has recently been suggested that neural network architectures could be interpreted as dynamical systems. Reciprocally, we show that our ODE representations are reminiscent of deep learning architectures. Furthermore, numerical analysis considerations on stability shed light on the assets and limitations of the method.

The method is illustrated on several chaotic discrete and continuous models of various dimensions, with or without noisy observations, with the goal to identify or improve the model dynamics, build a surrogate or reduced model, or produce forecasts from mere observations of the physical model.

Marc Bocquet et al.
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Marc Bocquet et al.
Marc Bocquet et al.
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Latest update: 26 May 2019
Publications Copernicus
Short summary
This paper describes an innovative way to use data assimilation to infer the dynamics of a physical system from its observation only. The method can operate with noisy and partial observation of the physical system. It acts as a deep learning technique specialised to dynamical models without the need for machine learning tools. The method is successfully tested on chaotic dynamical systems: the Lorenz-63, Lorenz-96, Kuramoto-Sivashinski models and a two-scale Lorenz model.
This paper describes an innovative way to use data assimilation to infer the dynamics of a...