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

Abstract

We propose a Bayesian inference methodology to evaluate unobservable parameters involved in multi-phasefield models to accurately predict the observed grain growth, such as in metals and alloys. This approach integrates models and a set of observational image data of grain structures. Because the image data set is not a time series, directly applying conventional inference techniques that require time series as the input data is difficult. The key idea in our methodology to overcome this difficulty is to construct a time series with an appropriate statistic that characterizes static image data of grain structures. Our methodology implements the empirical Bayes method. It can estimate not only a probability density function of the parameters but also an initial phase field, which is generally unobservable in real experiments. After validating the proposed method through numerical tests using synthetic data, we apply it to real experimental images of grain structures in a steel alloy. The proposed method properly estimates unobservable parameters along with their uncertainties and successfully selects the initial phase field that best explains the experimental data from among candidate initial phase fields.

A Phase Prediction Method for Pattern Formation in Time-Dependent Ginzburg-Landau Dynamics for Kinetic Ising Model without a priori Assumptions on Domain Patterns

“…One of such applications is parameter estimation in material-and statistical physics. Using the Bayesian inference methods, we can estimate the parameters of a system with huge degrees of freedom by relatively small observation/numerical data, e.g., 30 . Our method is expected to serve for such parameter estimations in various systems as the theoretical-and numerical basis by giving information on the phase for each parameter using a few computational costs, with physically justifiable reasons.…”

Materials Integration for Accelerating Research and Development of Structural Materials

“…The first group is to apply the Bayesian inference for model selection, which is proved to be useful to examine contributing factors in creep constituent equations, 27,28) ferrite transformation kinetics based on dilatometric measurement, 29) and the structure-property relationship with a dual-phase microstructure. 30) The second group is to utilize data assimilation methods for improving the prediction accuracy of various computational simulations such as phase field modeling 31) and welding process analysis. 32) Figure 5 shows an example of applying data A d v a n c e V i e w assimilation to determine the initial and materials parameters for texture evolution during recrystallization in Al alloys.…”

Data Assimilation in the Welding Process for Analysis of Weld Toe Geometry and Heat Source Model

“…In materials engineering, data assimilation is beginning to be used to estimate parameters such as the thermal conductivity in heat transfer analysis, 23) parameters in micromechanical modeling, 24,25) and the mobility of the phase-field simulation. [26][27][28] The present study aims to propose automatic characterization methods of weld toe geometry and heat source model by data assimilation techniques. In the analysis of weld toe geometry, the utilization of information criterion is examined to detect the position of the weld toe.…”