  Reservoir computing systems, a class of recurrent neural networks, have
recently been exploited for model-free, data-based prediction of the state
evolution of a variety of chaotic dynamical systems. The prediction horizon
demonstrated has been about half dozen Lyapunov time. Is it possible to
significantly extend the prediction time beyond what has been achieved so far?
We articulate a scheme incorporating time-dependent but sparse data inputs into
reservoir computing and demonstrate that such rare "updates" of the actual
state practically enable an arbitrarily long prediction horizon for a variety
of chaotic systems. A physical understanding based on the theory of temporal
synchronization is developed.
