  The basin of attraction is the set of initial points that will eventually
converge to some attracting set. Its knowledge is important in understanding
the dynamical behavior of a given dynamical system of interest. In this work,
we address the problem of reconstructing the basins of attraction of a
multistable system, using only labeled data. To this end, we view this problem
as a classification task and use a deep neural network as a classifier for
predicting the attractor that corresponds to any given initial condition.
Additionally, we provide a method for obtaining an approximation of the basin
boundary of the underlying system, using the trained classification model.
Finally, we provide evidence relating the complexity of the structure of the
basins of attraction with the quality of the obtained reconstructions, via the
concept of basin entropy. We demonstrate the application of the proposed method
on the Lorenz system in a bistable regime.
