  We present a machine-learning method for predicting sharp transitions in a
Hamiltonian phase diagram by extrapolating the properties of quantum systems.
The method is based on Gaussian Process regression with a combination of
kernels chosen through an iterative procedure maximizing the predicting power
of the kernels. The method is capable of extrapolating across the transition
lines. The calculations within a given phase can be used to predict not only
the closest sharp transition, but also a transition removed from the available
data by a separate phase. This makes the present method particularly valuable
for searching phase transitions in the parts of the parameter space that cannot
be probed experimentally or theoretically.
