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\begin{document}

\title{Data Assimilation Networks}



\author[1]{Pierre Boudier}%
\author[2]{Anthony Fillion}%
\author[2]{Serge Gratton}%
\author[3]{Selime Gurol}%
\author[2]{Sixin Zhang}%
\affil[1]{NVIDIA}%
\affil[2]{INP Toulouse}%
\affil[3]{Unknown}%


\vspace{-1em}



  
  \date{May 14, 2024}


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\begin{abstract}
Data assimilation (DA) aims at forecasting the state of a\\
dynamical system by combining a mathematical representation of the\\
system with noisy observations taking into account their
uncertainties.\\
State of the art methods are based on the Gaussian error statistics and
the linearization of the non-linear dynamics which may lead to
sub-optimal methods. In this\\
respect, there are still open questions how to improve these methods.\\
In this paper, we propose a \textbackslash{}textit\{fully data driven
deep learning architecture\}\\
generalizing recurrent Elman networks and data assimilation algorithms
which\\
approximate a sequence of prior and posterior densities conditioned on
noisy observations. By construction our approach can be used for general
nonlinear dynamics\\
and non-Gaussian densities.\\
On numerical experiments based on the well-known\\
Lorenz-95 system and with Gaussian error statistics, our architecture
achieves\\
comparable performance to EnKF on both the analysis and the propagation
of probability density functions of the system state at a given time
without using any explicit regularization technique.%
\end{abstract}%



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