  One of the major and unfortunately unforeseen sources of background for the
current generation of X-ray telescopes are few tens to hundreds of keV (soft)
protons concentrated by the mirrors. One such telescope is the European Space
Agency's (ESA) X-ray Multi-Mirror Mission (XMM-Newton). Its observing time lost
due to background contamination is about 40\%. This loss of observing time
affects all the major broad science goals of this observatory, ranging from
cosmology to astrophysics of neutron stars and black holes. The soft proton
background could dramatically impact future large X-ray missions such as the
ESA planned Athena mission (http://www.the-athena-x-ray-observatory.eu/).
Physical processes that trigger this background are still poorly understood. We
use a Machine Learning (ML) approach to delineate related important parameters
and to develop a model to predict the background contamination using 12 years
of XMM observations. As predictors we use the location of satellite, solar and
geomagnetic activity parameters. We revealed that the contamination is most
strongly related to the distance in southern direction, $Z$, (XMM observations
were in the southern hemisphere), the solar wind radial velocity and the
location on the magnetospheric magnetic field lines. We derived simple
empirical models for the first two individual predictors and an ML model which
utilizes an ensemble of the predictors (Extra Trees Regressor) and gives better
performance. Based on our analysis, future missions should minimize
observations during times associated with high solar wind speed and avoid
closed magnetic field lines, especially at the dusk flank region in the
southern hemisphere.
