Title: Copy the dynamics using a learning machine,
Abstract: Is it possible to generally construct a dynamical system to simulate a black
system without recovering the equations of motion of the latter? Here we show
that this goal can be approached by a learning machine. Trained by a set of
input-output responses or a segment of time series of a black system, a
learning machine can be served as a copy system to mimic the dynamics of
various black systems. It can not only behave as the black system at the
parameter set that the training data are made, but also recur the evolution
history of the black system. As a result, the learning machine provides an
effective way for prediction, and enables one to probe the global dynamics of a
black system. These findings have significance for practical systems whose
equations of motion cannot be approached accurately. Examples of copying the
dynamics of an artificial neural network, the Lorenz system, and a variable
star are given. Our idea paves a possible way towards copy a living brain.