Variational-Bayes-based Grain-size-distribution Inference for Robust Inverse Estimation of Small Angle Scattering

Abstract

In recent years, information technology to improve the efficiency of materials development has been actively studied. In this paper, we propose a method for estimating the microstructure of materials based on the variational Bayesian method, known as unsupervised machine learning, with a particular focus on the analysis of data from small-angle scattering (SAS) experiments. The estimation of the grain size distribution in a sample is often performed based on the experimental results. To automate this process, methods based on function fitting, such as the indirect Fourier transform, have been proposed. However, they suffer from the problem of over-fitting to measurement noise, which requires manual adjustment of the regularization term to suppress the over-fitting. In the proposed method, a flat prior probability distribution is set as prior knowledge of the grain size distribution to suppress over-fitting in a simple and theoretically clear manner. In this study, we evaluated the accuracy of the proposed method and the conventional method using three noisy data sets generated by simulations and confirmed that the proposed method gives more accurate results than the conventional method.