Copy the dynamics using a learning machine
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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.
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