Bayesian inference of grain growth prediction via multi-phase-field models
Bayesian inference of grain growth prediction via multi-phase-field models
复制标题
通过多相场模型进行晶粒生长预测的贝叶斯推理
DOI：
10.1103/physrevmaterials.3.053404
复制
发表时间：
2019
影响因子：
3.4
通讯作者：
and J. Inoue
中科院分区：
文献类型：
--
作者：
S. Ito;H. Nagao;T. Kurokawa;T. Kasuya;and J. Inoue
我们提出了一种贝叶斯推理方法来评估多相场模型中涉及的不可观测参数，以准确预测观察到的晶粒生长，例如金属和合金中的晶粒生长。该方法集成了模型和一组颗粒结构的观测图像数据。由于图像数据集不是时间序列，直接应用需要时间序列作为输入数据的传统推理技术是很困难的。我们克服这一困难的方法的关键思想是构建一个具有适当统计量的时间序列，该统计量可以表征颗粒结构的静态图像数据。我们的方法论采用经验贝叶斯方法。它不仅可以估计参数的概率密度函数，还可以估计实际实验中通常无法观测到的初始相场。通过使用合成数据的数值测试验证所提出的方法后，我们将其应用于钢合金中晶粒结构的真实实验图像。该方法正确估计了不可观测参数及其不确定性，并成功地从候选初始相场中选择了最能解释实验数据的初始相场。
We propose a Bayesian inference methodology to evaluate unobservable parameters involved in multi-phase-field 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.