PhAI: A deep learning approach to solve the crystallographic phase problem

For more than 100 years, X-ray crystallography has provided a unique view on the three-dimensional structure of atoms and molecules in crystals. However, to determine even the simplest structures now and a hundred years ago, one needs to overcome a mathematical hurdle for which the solution is not known even to this day. To reconstruct the 3-dimensional electron density map, from which the structure can be inferred, the complex structure factors F = |F| exp(iφ) of a sufficiently large number of diffracted reflections must be known. In a conventional diffraction experiment, only the amplitudes |F| are obtained, while the phases φ are lost. This is the crystallographic phase problem. Seventy years of research has established successful ab initio phasing methods such as direct methods and charge flipping. However, these methods are limited to atomic- resolution data, complicating structure determination from weakly-scattering crystals. Here, we show that a neural network can solve the crystallographic phase problem at a resolution of only 2 Å. We have developed an approach to generate millions of artificial structures and respective diffraction data for training of a neural network. We demonstrate that ab initio phasing based on this neural network is possible using 10 % to 20 % of the data needed for present-day methods, breaking the paradigm that atomic resolution is necessary for ab initio structure solution. The current neural network works in common centrosymmetric space groups and for modest unit cell dimensions, and suggests that neural networks can be used to solve the phase problem in the general case. This approach will enable structure solution for weakly-scattering crystals such as metal-organic frameworks or nanometer-sized crystals investigated using electron diffraction.