  We investigate the extent to which a two-level quantum system subjected to an
external time-dependent drive can be characterized by supervised learning. We
apply this approach to the case of bang-bang control and the estimation of the
offset and the final distance to a given target state. For any control
protocol, the goal is to find the mapping between the offset and the distance.
This mapping is interpolated using a neural network. The estimate is global in
the sense that no a priori knowledge is required on the relation to be
determined. Different neural network algorithms are tested on a series of data
sets. We show that the mapping can be reproduced with very high precision in
the direct case when the offset is known, while obstacles appear in the
indirect case starting from the distance to the target. We point out the limits
of the estimation procedure with respect to the properties of the mapping to be
interpolated. We discuss the physical relevance of the different results.
