Derivation and discovery of physical dynamics inherent in big data is one of the most major purposes of machine learning (ML) in the field of modern natural science. In the materials science, phase diagrams are often called as “road maps” to perfectly understand the conditions for phase formation and/or transformation in any material system caused by the associated thermodynamics. In this paper, we report a numerical experiment investigating whether the underlying thermodynamics can be derived from the big data constructed of local spatial composition and phase distribution data along with the help of ML. The artificial data analysed have been created assuming a steel composition based on the calculation phase diagram (CALPHAD) thermodynamics combined with the order-statistics-based sampling model. The hypothetical procedures of data acquisition assumed in this numerical experiment are as follows; (i) obtaining local analysis data on the composition and phase distribution in the same observation area using instruments such as electron probe micro analyser (EPMA) and electron backscattering diffraction (EBSD), and (ii) training the classification model based on a ML algorithm with compositional data as input and the phase data as output. The accuracies of the reconstructed phase diagrams have been estimated for three ML algorithms, i.e. support vector machine (SVM), random forest, and multilayer perceptron (MLP). The phase diagrams predicted using SVM and MLP are found to be adequately consistent with those of the CALPHAD method. We have also investigated the regression performance of the continuous data involved in the CALPHAD thermodynamics, such as the phase fractions of body-centred cubic, face-centred cubic, and cementite phases. Compared with the ML algorithms, the CALPHAD method is found to show superior predictive performance since it is based on the sophisticated physical model.

推导和发现大数据中固有的物理动力学是现代自然科学领域机器学习 (ML) 的主要目的之一。在材料科学中，相图通常被称为“路线图”，以完美地理解由相关热力学引起的任何材料系统中相形成和/或转变的条件。在本文中，我们报告了一个数值实验，研究是否可以在 ML 的帮助下从由局部空间组成和相分布数据构建的大数据中导出潜在的热力学。分析的人工数据是假设钢成分基于计算相图 (CALPHAD) 热力学结合基于顺序统计的采样模型而创建的。本次数值实验中假设的数据采集过程如下：(i) 使用电子探针微量分析仪 (EPMA) 和电子背散射衍射 (EBSD) 等仪器获取同一观测区域内成分和相分布的局部分析数据，以及 (ii) 基于 ML 算法训练分类模型以成分数据作为输入，相位数据作为输出。已为三种机器学习算法，即支持向量机 (SVM)、随机森林和多层感知器 (MLP) 估计了重建相图的精度。发现使用 SVM 和 MLP 预测的相图与 CALPHAD 方法的相图完全一致。我们还研究了 CALPHAD 热力学中涉及的连续数据的回归性能，例如体心立方、面心立方和渗碳体相的相分数。与 ML 算法相比，发现 CALPHAD 方法显示出优越的预测性能，因为它基于复杂的物理模型。