  The behavior of recurrent neural network for the data-driven simulation of
noisy dynamical systems is studied by training a set of Long Short-Term Memory
Networks (LSTM) on the Mackey-Glass time series with a wide range of noise
level. It is found that, as the training noise becomes larger, LSTM learns to
depend more on its autonomous dynamics than the noisy input data. As a result,
LSTM trained on noisy data becomes less susceptible to the perturbation in the
data, but has a longer relaxation timescale. On the other hand, when trained on
noiseless data, LSTM becomes extremely sensitive to a small perturbation, but
is able to adjusts to the changes in the input data.
