Rapid, Comprehensive Search of Crystalline Phases from X-ray Diffraction in Seconds via GPU-Accelerated Bayesian Variational Inference

In analysis of X-ray diffraction data, identifying the crystalline phase is important for interpreting the material. The typical method is identifying the crystalline phase from the coincidence of the main diffraction peaks. This method identifies crystalline phases by matching them as individual crystalline phases rather than as combinations of crystalline phases, in the same way as the greedy method. If multiple candidates are obtained, the researcher must subjectively select the crystalline phases. Thus, the identification results depend on the researcher's experience and knowledge of materials science. To solve this problem, we have developed a Bayesian estimation method to identify the combination of crystalline phases, taking the entire profile into account. This method estimates the Bayesian posterior probability of crystalline phase combinations by performing an approximate exhaustive search of all possible combinations. It is a method for identifying crystalline phases that takes into account all peak shapes and phase combinations. However, it takes a few hours to obtain the analysis results. The aim of this study is to develop a Bayesian method for crystalline phase identification that can provide results in seconds, which is a practical calculation time. We introduce variational sparse estimation and GPU computing. Our method is able to provide results within 10 seconds even when analysing $2^{50}$ candidate crystalline phase combinations. Furthermore, the crystalline phases identified by our method are consistent with the results of previous studies that used a high-precision algorithm.