  We present a supervised learning method to learn the propagator map of a
dynamical system from partial and noisy observations. In our computationally
cheap and easy-to-implement framework a neural network consisting of random
feature maps is trained sequentially by incoming observations within a data
assimilation procedure. By employing Takens' embedding theorem, the network is
trained on delay coordinates. We show that the combination of random feature
maps and data assimilation, called RAFDA, outperforms standard random feature
maps for which the dynamics is learned using batch data.
