  Can a neural network trained by the time series of system A be used to
predict the evolution of system B? This problem, knowing as transfer learning
in a broad sense, is of great importance in machine learning and data mining,
yet has not been addressed for chaotic systems. Here we investigate transfer
learning of chaotic systems from the perspective of synchronization-based state
inference, in which a reservoir computer trained by chaotic system A is used to
infer the unmeasured variables of chaotic system B, while A is different from B
in either parameter or dynamics. It is found that if systems A and B are
different in parameter, the reservoir computer can be well synchronized to
system B. However, if systems A and B are different in dynamics, the reservoir
computer fails to synchronize with system B in general. Knowledge transfer
along a chain of coupled reservoir computers is also studied, and it is found
that, although the reservoir computers are trained by different systems, the
unmeasured variables of the driving system can be successfully inferred by the
remote reservoir computer. Finally, by an experiment of chaotic pendulum, we
show that the knowledge learned from the modeling system can be used to predict
the evolution of the experimental system.
