5-18. Materials genome based on hierarchical microstructures

Zhiheng Huang^1* and Xiaodong Xiang²

1.School of Materials Science and Engineering, Sun Yat-sen University

2.Department of Materials Science and Engineering, Southern University of Science and Technology

Abstract: Multiscale material microstructures obtained either by experimental characterization or modeling and simulation are of two or three-dimensional digital images, but the feature pixels or structural units may exhibit a myriad of variations, for examples, translation, rotation, deformation and etc., such that recognizing a particular microstructure by a direct image comparison pixel by pixel is sheerly not feasible. Therefore, the goal of microstructure recognition can only be achieved by extracting and classifying the invariant features. In general, the phase constituents in microstructural images are separated by interfaces and therefore discontinuity exists. Digital image processing based on Fourier analysis is therefore not the best choice. Meanwhile, the information on spatial distribution of microstructure is lost during a Fourier transformation. On the other hand, wavelet analysis exhibits a multi-resolution nature and can ideally deal with discontinuities in digital signals. Hence an inherent match connects wavelets with multiscale microstructures. In the high-dimension microstructural space, the mapping of feature extraction should on one hand keep the topological structure of the space unchanged and on the other hand be contractive. Studies on the mathematical principles of deep learning have proven that wavelet scattering satisfies such requirements. A wavelet scattering path can extract hierarchical features of a microstructure. The perfect match of wavelet scattering with microstructure physics is the most important advantage of this method. Table I shows the result of the second layer of a wavelet scattering on three different material microstructures.

Although the materials genome initiative has made important progress since 2011, multiscale microstructures, as the core of material genome, are still expecting for better quantification methods and descriptors. Systematically utilizing wavelet multiresolution analysis on microstructures and adopting wavelet scattering to extract hierarchical features is the method proposed in this work. Material genomes built upon such hierarchical microstructure data can reveal the intrinsic PSPP relationship and correlation between multiscale physical processes and hierarchical microstructures.

Keywords: Materials genome; multiscale microstructure; multiresolution wavelet analysis; wavelet scattering; hierarchical materials informatics

摘要：本文采用多分辨率小波分析研究微结构，使用小波散射系统构建材料层级微结构特征数据，并在此基础上采用无监管自组织映射和监管机器学习方法发现材料基因。

实验表征或模拟仿真所获得的材料多尺度微结构为二维或者三维图像，然而图像中的特征像素或者结构单元可能表现出多种变化，例如平移、旋转、变形等，因此通过像素的直接对比来识别微结构的各种变化是不可行的。微结构的识别应基于它们不可变特征的提取和分类。微结构图像中的相由界面分隔，存在不连续性，因此傅立叶分析不是最佳方法，微结构特征的空间分布信息也会在傅立叶变换中丢失。小波具有多分辨率且可处理不连续性，因此多尺度微结构与小波具有天然的匹配性。在高维微结构空间中，特征提取映射应保持微结构空间的拓扑结构且应具有空间收缩性，对深度学习数学机理的研究表明小波散射具备该属性。一个小波散射路径可提取微结构的层级量化指标，小波散射与微结构物理的匹配性是该方法的最大优势。表一展示了三种微结构的小波散射第二层量化表征结果。小波散射第二层量化结果坐标轴刻度为像素大小，横轴方向六图为角度扫描结果，微结构与小波方向一致则结果较大，纵轴五图为尺度扫描，从下至上小波尺度逐步减小。

系统使用多分辨率小波分析材料微结构以及使用小波散射提取材料层级微结构特征是本文首创，以此为基础构建的材料基因能从本质上揭示PSPP关系以及多尺度物理过程与层级微结构的关联。

关键词：材料基因；多尺度微结构；多分辨率小波分析；小波散射；层级材料信息学