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Application of artificial neural networks to the crystallographic phase problem (Bachelor thesis)

Moschou, Dionysia

X-ray crystallography is a tool used in order to determine small structures such as proteins. The atoms in a crystal under study cause a beam of incident X-rays to diffract and give a diffraction pattern. In order to produce a 3-dimensional picture of the density of electrons within a crystal, a crystallographer needs the amplitudes and also the phases of the diffracted waves. The information of those phases is lost resulting in the phase problem. Algorithmic operations such as direct methods have been developed to overcome this obstacle. These methods suggest direct relationships between the structure factors of a crystal. Artificial Neural Networks are computational models. They are presented as systems of interconnected neurons which exchange messages between each other. These connections have numeric weights that can be tuned based on experience, making them adaptive to inputs and capable of learning, therefore estimate the phases of the diffracted waves using only the observed intensities. The objective was for a network to be constructed in order that it learns the necessary algorithmic operations to estimate the crystallographic phase by means of only the directly observed experimental data. If neural networks could learn relationships as those used in direct methods, it would greatly enhance the work of crystallographers.