  Can noise be beneficial to machine-learning prediction of chaotic systems?
Utilizing reservoir computers as a paradigm, we find that injecting noise to
the training data can induce a stochastic resonance with significant benefits
to both short-term prediction of the state variables and long-term prediction
of the attractor of the system. A key to inducing the stochastic resonance is
to include the amplitude of the noise in the set of hyperparameters for
optimization. By so doing, the prediction accuracy, stability and horizon can
be dramatically improved. The stochastic resonance phenomenon is demonstrated
using two prototypical high-dimensional chaotic systems.
