  A novel method, based on the combination of data assimilation and machine
learning is introduced. The new hybrid approach is designed for a two-fold
scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting
their future states. The method consists in applying iteratively a data
assimilation step, here an ensemble Kalman filter, and a neural network. Data
assimilation is used to optimally combine a surrogate model with sparse noisy
data. The output analysis is spatially complete and is used as a training set
by the neural network to update the surrogate model. The two steps are then
repeated iteratively. Numerical experiments have been carried out using the
chaotic 40-variables Lorenz 96 model, proving both convergence and statistical
skill of the proposed hybrid approach. The surrogate model shows short-term
forecast skill up to two Lyapunov times, the retrieval of positive Lyapunov
exponents as well as the more energetic frequencies of the power density
spectrum. The sensitivity of the method to critical setup parameters is also
presented: the forecast skill decreases smoothly with increased observational
noise but drops abruptly if less than half of the model domain is observed. The
successful synergy between data assimilation and machine learning, proven here
with a low-dimensional system, encourages further investigation of such hybrids
with more sophisticated dynamics.
