  Machine learning methods have proved to be useful for the recognition of
patterns in statistical data. The measurement outcomes are intrinsically random
in quantum physics, however, they do have a pattern when the measurements are
performed successively on an open quantum system. This pattern is due to the
system-environment interaction and contains information about the relaxation
rates as well as non-Markovian memory effects. Here we develop a method to
extract the information about the unknown environment from a series of
projective single-shot measurements on the system (without resorting to the
process tomography). The method is based on embedding the non-Markovian system
dynamics into a Markovian dynamics of the system and the effective reservoir of
finite dimension. The generator of Markovian embedding is learned by the
maximum likelihood estimation. We verify the method by comparing its prediction
with an exactly solvable non-Markovian dynamics. The developed algorithm to
learn unknown quantum environments enables one to efficiently control and
manipulate quantum systems.
