X-ray crystallography provides a distinctive view on the three-dimensional structure of crystals. To reconstruct the electron density map, the complex structure factors [Formula: see text] of a sufficiently large number of diffracted reflections must be known. In a conventional experiment, only the amplitudes [Formula: see text] are obtained, and the phases ϕ are lost. This is the crystallographic phase problem. In this work, we show that a neural network, trained on millions of artificial structure data, can solve the phase problem at a resolution of only 2 angstroms, using only 10 to 20% of the data needed for direct methods. The network works in common space groups and for modest unit-cell dimensions and suggests that neural networks could be used to solve the phase problem in the general case for weakly scattering crystals.