Combining Data Assimilation and Machine Learning to emulate a numerical model from noisy and sparse observations.

Is it possible to emulate a numerical model from noisy and sparse observations? How realisticand skillful can it be? A popular way to produce data-driven models from a set of observations is to applymachine-learning methods. These approaches proved efficient for chaotic systemsusing various machine learning algorithms such as, for instance, deep-learningor reservoir computing. In most of previous works, these approaches were usedwith a noisy-free, completely observed, state vector, and their performance wasevaluated on short-term predictability skills. When it comes to noisy and sparseobservations, data assimilation techniques provide the natural tools to produce an optimalestimation of the state of a system, provided a numerical model, is available (thoughimperfect). In this work, we consider the case in which noisy and partial observations of a givenphenomena are available but the evolution model is unknown. The idea is to applymachine-learning and data assimilation algorithms alternatively to learn the underlyingdynamics of the system. First, the data assimilation procedure completes the state estimate,which is then used as a training set for machine learning. Reciprocally, the machinelearning-based model is used as the forward dynamical model in the data assimilationframework. The sequence is reiterated with increasing complexity of the machine learningmodel. This combined approach is tested numerically in a twin experiments setup with chaoticmodels. The machine learning algorithm used in this work is a convolutional neural networkarchitecture (CNN) whereas the data assimilation scheme is an ensemble Kalman filter (usingthe finite-size variant to avoid the inflation: EnKF-N). The resulting CNN showed bothforecast skills and abilities to reproduce the "climate" (i.e. spectral properties and statisticalmoments) of the underlying dynamical model on long-term simulations. Perspectives towardslarge-scale systems will be discussed on the basis of the benchmarks presented. [ABSTRACT FROM AUTHOR]