Is it possible to emulate a numerical model from noisy and sparse observations? How realistic and skilful can it be? Recent progress in machine learning has shown how to forecast a model from observations. We will show that by leveraging on data assimilation techniques, it is possible to produce realistic and skilful surrogate models of the underlying dynamics given sparse and noisy observations. The approach is tested with several chaotic systems. The surrogate model shows both forecast skills and abilities to reproduce the “climate” (i.e. spectral properties and statistical moments) of the underlying dynamical model on long-term simulations.