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This work demonstrates that, for a simple case of 10 randomly positionedatoms, a neural network can be trained to infer atomic coordinates fromPatterson maps. The network was trained entirely on synthetic data. For thetraining set, the network outputs were 3D maps of randomly positioned atoms.From each output map, a Patterson map was generated and used as input to thenetwork. The network generalized to cases not in the test set, inferring atompositions from Patterson maps.  A key finding in this work is that the Patterson maps presented to thenetwork input during training must uniquely describe the atomic coordinatesthey are paired with on the network output or the network will not train and itwill not generalize. The network cannot train on conflicting data. Avoidingconflicts is handled in 3 ways: 1. Patterson maps are invariant to translation.To remove this degree of freedom, output maps are centered on the average oftheir atom positions. 2. Patterson maps are invariant to centrosymmetricinversion. This conflict is removed by presenting the network output with boththe atoms used to make the Patterson Map and their centrosymmetry-relatedcounterparts simultaneously. 3. The Patterson map does not uniquely describe aset of coordinates because the origin for each vector in the Patterson map isambiguous. By adding empty space around the atoms in the output map, thisambiguity is removed. Forcing output atoms to be closer than half the outputbox edge dimension means the origin of each peak in the Patterson map must bethe origin to which it is closest.

From Patterson Maps to Atomic Coordinates: Training a Deep Neural Network to Solve the Phase Problem for a Simplified Case