  In applications of dynamical systems, situations can arise where it is
desired to predict the onset of synchronization as it can lead to
characteristic and significant changes in the system performance and behaviors,
for better or worse. In experimental and real settings, the system equations
are often unknown, raising the need to develop a prediction framework that is
model free and fully data driven. We contemplate that this challenging problem
can be addressed with machine learning. In particular, exploiting reservoir
computing or echo state networks, we devise a "parameter-aware" scheme to train
the neural machine using asynchronous time series, i.e., in the parameter
regime prior to the onset of synchronization. A properly trained machine will
possess the power to predict the synchronization transition in that, with a
given amount of parameter drift, whether the system would remain asynchronous
or exhibit synchronous dynamics can be accurately anticipated. We demonstrate
the machine-learning based framework using representative chaotic models and
small network systems that exhibit continuous (second-order) or abrupt
(first-order) transitions. A remarkable feature is that, for a network system
exhibiting an explosive (first-order) transition and a hysteresis loop in
synchronization, the machine learning scheme is capable of accurately
predicting these features, including the precise locations of the transition
points associated with the forward and backward transition paths.
