  We have trained a deep (convolutional) neural network to predict the
ground-state energy of an electron in four classes of confining two-dimensional
electrostatic potentials. On randomly generated potentials, for which there is
no analytic form for either the potential or the ground-state energy, the
neural network model was able to predict the ground-state energy to within
chemical accuracy, with a median absolute error of 1.49 mHa. We also
investigate the performance of the model in predicting other quantities such as
the kinetic energy and the first excited-state energy of random potentials.
