  We explore the influence of precision of the data and the algorithm for the
simulation of chaotic dynamics by neural networks techniques. For this purpose,
we simulate the Lorenz system with different precisions using three different
neural network techniques adapted to time series, namely reservoir computing
(using ESN), LSTM and TCN, for both short and long time predictions, and assess
their efficiency and accuracy. Our results show that the ESN network is better
at predicting accurately the dynamics of the system, and that in all cases the
precision of the algorithm is more important than the precision of the training
data for the accuracy of the predictions. This result gives support to the idea
that neural networks can perform time-series predictions in many practical
applications for which data are necessarily of limited precision, in line with
recent results. It also suggests that for a given set of data the reliability
of the predictions can be significantly improved by using a network with higher
precision than the one of the data.
