  The rectangular collocation approach makes it possible to solve the
Schr\"odinger equation with basis functions that do not have amplitude in all
regions in which wavefunctions have significant amplitude. Collocation points
can be restricted to a small region of space. As no integrals are computed,
there are no problems due to discontinuities in the potential, and there is no
need to use integrable basis functions. In this paper, we show, for the
Kohn-Sham equation, that machine learning can be used to drastically reduce the
size of the collocation point set. This is demonstrated by solving the
Kohn-Sham equations for CO and H2O. We solve the Kohn-Sham equation on a given
effective potential which is a critical part of all DFT calculations, and
monitor orbital energies and orbital shapes. We use a combination of Gaussian
process regression and a genetic algorithm to reduce the collocation point set
size by more than an order of magnitude (from about 51,000 points to 2,000
points) while retaining mHartree accuracy.
