From Patterson Maps to Atomic Coordinates: Training a Deep Neural Network to Solve the Phase Problem for a Simplified Case
Abstract
This work demonstrates that, for a simple case of 10 randomly positioned atoms, a neural network can be trained to infer atomic coordinates from Patterson maps. The network was trained entirely on synthetic data. For the training 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 the network. The network generalized to cases not in the test set, inferring atom positions from Patterson maps. A key finding in this work is that the Patterson maps presented to the network input during training must uniquely describe the atomic coordinates they are paired with on the network output or the network will not train and it will not generalize. The network cannot train on conflicting data. Avoiding conflicts 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 of their atom positions. 2. Patterson maps are invariant to centrosymmetric inversion. This conflict is removed by presenting the network output with both the atoms used to make the Patterson Map and their centrosymmetry-related counterparts simultaneously. 3. The Patterson map does not uniquely describe a set of coordinates because the origin for each vector in the Patterson map is ambiguous. By adding empty space around the atoms in the output map, this ambiguity is removed. Forcing output atoms to be closer than half the output box edge dimension means the origin of each peak in the Patterson map must be the origin to which it is closest.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2020
- DOI:
- 10.48550/arXiv.2003.13767
- arXiv:
- arXiv:2003.13767
- Bibcode:
- 2020arXiv200313767H
- Keywords:
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- Computer Science - Machine Learning;
- Physics - Atomic Physics;
- Statistics - Machine Learning
- E-Print:
- This work is a personal project of the author. The opinions expressed in this article are the author's own and do not reflect the view of the National Institutes of Health, the Department of Health and Human Services, or the United States government. Email: hurwitz dot david at gmail dot com