Dynamical process of learning chaotic time series by neural networks

We report the result of computer simulations on the learning process of temporal series by artificial neural networks. In our simulation, we used a feedforward neural network model with 4-layers to study the capability and dynamical learning process of chaotic time series produced by triangular maps. We found a critical time (t_cr) at which the learning process proceeds abruptly. We also found that the critical time (t_cr) is shorter, the larger the initial deviation from the target of learning. We provide detailed discussion about the learning process to explain these interesting phenomena, and a new order parameter coherency is introduced to characterize these processes.