Deep-learning and the Phase Problem

Here is a paper I wrote about my efforts to apply deep-learning to the phase problem:
From Patterson Maps to Atomic Coordinates: Training a Deep Neural Network to Solve the Phase Problem for a Simplified Case

Here is a video I made that gives introductory material about the subject:

Here is a video I made that describes the work itself:


Here are the slides that were used in the videos:

Here is all the code I developed for this work:
https://github.com/davidihu/PattersonMaps

Here is the short story:
A neural network was trained on many cases and learned to generalize for cases not in the training set. There are some important considerations that must be taken into account or the network will not train or generalize. These considerations are described in detail in the paper and the second video.

For each training case, an electron density map was calculated for 10 randomly-positioned atoms. A Patterson Map was calculated from this density map and placed on the neural network input. Then, electron density was calculated for 10 atoms related by centrosymmetry to the first 10 atoms. The 2 density maps were added together and placed on the network output. The network trained on many such cases.

The 2 figures above show an example of how the trained neural network performed for a case not in the training set. The left image shows electron density for 10 randomly positioned atoms (red) plus their 10 centro-symmetry related atoms (blue). A Patterson Map was calculated from the red density and placed on the neural network input. The trained neural network produced the image on the right which is strikingly similar to the left image, demonstrating that the network learned to generalize for cases not in the training set. Much more detail is in the paper and videos.