Data-driven reconstruction of chaotic dynamics using data assimilation and machine learning

Marc Bocquet, École des Ponts ParisTech, France - 11:15

Recent progress in machine learning has shown how to forecast and, to some extent, learn the dynamics of a model from observations, resorting in particular to residual neural networks. These approaches are often limited by the need to have a dense observational network or at least regularly subsampled observations. Our proposal is to rely on data assimilation techniques originally developed to best accommodate dynamical models with sparse and noisy data. We demonstrate that by combining machine learning with data assimilation techniques, it is possible to produce realistic and skilful surrogate models of the underlying dynamics given sparse and noisy observations. Assuming either locality or the use of convolutional neural networks, we show how the method can be extended to higher-dimensional dynamics. We propose algorithms, based in particular on the expectation maximisation technique, that are needed to numerically solve this generalised data assimilation problem where the state trajectory, the model and the model error statistics are all solved for. These methods are illustrated on two low-order chaotic models.

M. Bocquet1, J. Brajard2,3, A. Carrassi4,5 and L. Bertino3

(1) CEREA joint laboratory École des Ponts ParisTech and EdF R&D, Université Paris-Est, France

(2) Sorbonne University, CNRS-IRD-MNHN, LOCEAN, Paris, France

(3) Nansen Environmental and Remote Sensing Center, Bergen, Norway

(4) Department of meteorology, University of Reading, United Kingdom

(5) Mathematical institute, University of Utrecht, The Netherlands

Invitied by Jana de Wiljes