  This article presents an approach to the two-dimensional Schr\"odinger
equation based on automatic learning methods with neural networks. It is
intended to determine the ground state of a particle confined in any
two-dimensional potential, starting from the knowledge of the solutions to a
large number of arbitrary sample problems. A network architecture with two
hidden layers is proposed to predict the wave function and energy of the ground
state. Several accuracy indicators are proposed for validating the estimates
provided by the neural network. The testing of the trained network is done by
applying it to a large set of confinement potentials different from those used
in the learning process. Some particular cases with symmetrical potentials are
solved as concrete examples, and a good network prediction accuracy is found.
