  Forecasting the dynamics of chaotic systems from the analysis of their output
signals is a challenging problem with applications in most fields of modern
science. In this work, we use a laser model to compare the performance of
several machine learning algorithms for forecasting the amplitude of upcoming
emitted chaotic pulses. We simulate the dynamics of an optically injected
semiconductor laser that presents a rich variety of dynamical regimes when
changing the parameters. We focus on a particular dynamical regime that can
show ultra-high intensity pulses, reminiscent of rogue waves. We compare the
goodness of the forecast for several popular methods in machine learning,
namely deep learning, support vector machine, nearest neighbors and reservoir
computing. Finally, we analyze how their performance for predicting the height
of the next optical pulse depends on the amount of noise and the length of the
time-series used for training.
