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Learning Variational Data Assimilation Models and Solvers

Ronan Fablet 1, 2, * Bertrand Chapron 3 Lucas Drumetz 1, 2 Etienne Mémin 4 Olivier Pannekoucke 5 François Rousseau 6, 7 
* Corresponding author
1 Lab-STICC_IMTA_CID_TOMS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
4 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique , INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using both supervised and unsupervised strategies. Our numerical experiments on Lorenz-63 and Lorenz-96 systems report significant gain w.r.t. a classic gradient-based minimization of the variational cost both in terms of reconstruction performance and optimization complexity. Intriguingly, we also show that the variational models issued from the true Lorenz-63 and Lorenz-96 ODE representations may not lead to the best reconstruction performance. We believe these results may open new research avenues for the specification of assimilation models in geoscience.
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Ronan Fablet, Bertrand Chapron, Lucas Drumetz, Etienne Mémin, Olivier Pannekoucke, et al.. Learning Variational Data Assimilation Models and Solvers. Journal of Advances in Modeling Earth Systems, American Geophysical Union, 2021, 13, pp.article n° e2021MS002572. ⟨10.1029/2021MS002572⟩. ⟨hal-02906798⟩

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