  Given a segment of time series of a system at a particular set of parameter
values, can one infers the global behavior of the system in its parameter
space? Here we show that by using a learning machine we can achieve such a goal
to a certain extent. It is found that following an appropriate training
strategy that monotonously decreases the cost function, the learning machine in
different training stage can mimic the system at different parameter set.
Consequently, the global dynamical properties of the system is subsequently
revealed, usually in the simple-to-complex order. The underlying mechanism is
attributed to the training strategy, which causes the learning machine to
collapse to a qualitatively equivalent system of the system behind the time
series. Thus, the learning machine opens up a novel way to probe the global
dynamical properties of a black-box system without artificially establish the
equations of motion. The given illustrating examples include a representative
model of low-dimensional nonlinear dynamical systems and a spatiotemporal model
of reaction-diffusion systems.
