  Machine learning algorithms designed to learn dynamical systems from data can
be used to forecast, control and interpret the observed dynamics. In this work
we exemplify the use of one of such algorithms, namely Koopman operator
learning, in the context of open quantum system dynamics. We will study the
dynamics of a small spin chain coupled with dephasing gates and show how
Koopman operator learning is an approach to efficiently learn not only the
evolution of the density matrix, but also of every physical observable
associated to the system. Finally, leveraging the spectral decomposition of the
learned Koopman operator, we show how symmetries obeyed by the underlying
dynamics can be inferred directly from data.
