Learnability of times series

Neural networks can be trained to learn the time series of a dynamical system. They can then be used to predict the next value of a given series. The example used is the chaotic quadratic map. The authors study to what extent the network generalizes the correct rule from the training set. It is concluded that a network can discover the correct law if its architecture can accommodate it. Otherwise it provides an approximation whose accuracy deteriorates quickly in long term predictions