Bayesian inference of grain growth prediction via multi-phase-field models

We propose a Bayesian inference methodology to evaluate unobservable parameters involved in multi-phase-field models with the aim of accurately predicting the observed grain growth, such as in metals and alloys. This approach integrates models and a set of observational image data of grain structures. Since the set of image data is not a time series, directly applying conventional inference techniques that require time series as the input data is difficult. Our key idea is to construct a time series with an appropriate statistic that characterizes static image data of grain structures. The empirical Bayes method estimates not only a probability density function of the parameters but also an initial phase-field, which is generally unobservable in real experiments. The proposed method is confirmed to estimate, from real experimental images of grain structures in a steel alloy, unobservable parameters together with their uncertainties, and successfully selects the initial phase-field that best explains the experimental data from among candidate initial phase-fields.