  Recently, there has been significant advancement in the machine learning (ML)
approach and its application to diverse systems ranging from complex to quantum
systems. As one of such systems, a coupled-oscillators system exhibits
intriguing collective behaviors, synchronization phase transitions, chaotic
behaviors and so on. Even though traditional approaches such as analytical and
numerical methods enable to understand diverse properties of such systems, some
properties still remain unclear. Here, we applied the ML approach to such
systems particularly described by the Kuramoto model, with the aim of resolving
the following intriguing problems, namely determination of the transition point
and criticality of a hybrid synchronization transition; understanding network
structures from chaotic patterns; and comparison of ML algorithms for the
prediction of future chaotic behaviors. The proposed method is expected to be
useful for further problems such as understanding a neural network structure
from electroencephalogram signals.
