  Understanding how the structure of materials affects their properties is a
cornerstone of materials science and engineering. However, traditional methods
have struggled to accurately describe the quantitative structure-property
relationships for complex structures. In our study, we bridge this gap by
leveraging machine learning to analyze images of materials' microstructures,
thus offering a novel way to understand and predict the properties of materials
based on their microstructures. We introduce a method known as FAGC (Feature
Augmentation on Geodesic Curves), specifically demonstrated for Cu-Cr-Zr
alloys. This approach utilizes machine learning to examine the shapes within
images of the alloys' microstructures and predict their mechanical and
electronic properties. This generative FAGC approach can effectively expand the
relatively small training datasets due to the limited availability of materials
images labeled with quantitative properties. The process begins with extracting
features from the images using neural networks. These features are then mapped
onto the Pre-shape space to construct the Geodesic curves. Along these curves,
new features are generated, effectively increasing the dataset. Moreover, we
design a pseudo-labeling mechanism for these newly generated features to
further enhance the training dataset. Our FAGC method has shown remarkable
results, significantly improving the accuracy of predicting the electronic
conductivity and hardness of Cu-Cr-Zr alloys, with R-squared values of 0.978
and 0.998, respectively. These outcomes underscore the potential of FAGC to
address the challenge of limited image data in materials science, providing a
powerful tool for establishing detailed and quantitative relationships between
complex microstructures and material properties.
