Towards Microstructural State Variables in Materials Systems

TL;DR

This paper develops machine learning methods to efficiently extract meaningful low-dimensional variables from complex microstructural image data, aiding in understanding and modeling material properties.

Contribution

It introduces local dimensionality estimation techniques and autoencoder-based methods to reduce microstructural data complexity and identify key state variables.

Findings

Nearest neighbor dimensionality estimates are consistent for natural images.

Manhattan distance reduces systematic errors in low-bit microstructural images.

Autoencoders effectively reconstruct microstructural generator spaces and identify sparse state variables.

Abstract

The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large microstructural datasets. There is a need for machine learning techniques that can manage data complexity by capturing the maximal amount of information about the microstructure using the least number of variables. This paper aims to formulate dimensionality and state variable estimation techniques focused on reducing microstructural image data. It is shown that local dimensionality estimation based on nearest neighbors tend to give consistent dimension estimates for natural images for all p-Minkowski distances. However, it is found that dimensionality estimates have a systematic error for low-bit depth microstructural images. The use of Manhattan distance to alleviate this issue is demonstrated. It is also shown that stacked autoencoders can reconstruct the generator space of high dimensional microstructural data and provide a sparse set of state variables to fully describe the variability in material microstructures.