Gradient Observations in Global Structure Search with Bayesian Optimization

Abstract

Knowledge of the microscopic atomic structure of a material gives insight into its macroscopic properties, which facilitates tailoring of the material for specific functionalities. Potential obstacles encountered during direct experimentation can be avoided using computational simulations to model atomic structures. The space of possible atomic configurations can be mapped onto a potential energy surface, with lower energies indicating more stable configurations. This surface can be explored to determine stable states of the material. However, the exploration typically demands a high number of configuration samples. The Bayesian optimization structure search (BOSS) method alleviates the exploration by keeping the number of samples required to a minimum. Atomic simulations often calculate gradients in addition to energies of atomic systems, which means data points that are richer in information content. Therefore, including gradient observations should theoretically further reduce the number of configuration samples required by the BOSS method to find stable states. The goal of my research was to implement the functionality of including gradient observations into the BOSS method, and to investigate the effect the functionality has on the exploration. The implementation involved the writing of relevant mathematical concepts into software, specifically two Python packages. The effect the functionality has on the exploration was examined by applying the augmented BOSS method on two computational experiments that both modeled different atomic systems. The results from the computational experiments suggest that including gradient observations reduces the amount of data required by the BOSS method, by as much as approximately 66 % in some cases. However, the inclusion of gradient observations make certain matrix operations scale as O(N3D3), for N data points and D dimensions. This resulted in a slower process in some cases, even though the amount of data required was reduced. Therefore, there is a compromise between amount of data required and time taken by the BOSS method. The inclusion of gradient observations will likely be most beneficial for slower simulations—such as those of higher fidelity.