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Dependence of Microstructure Classification Accuracy on Crystallographic Data Representation

Shrunal Pothagoni, Dylan Miley, Tyrus Berry, Jeremy K. Mason, Benjamin Schweinhart

TL;DR

Four representations of orientation information are examined and are used with convolutional neural networks to classify five synthetic microstructures with varying textures and grain geometries, and a spectral embedding of crystallographic orientations in a space that respects the crystallographic symmetries performs by far the best.

Abstract

Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant microstructural features more efficiently and impartially than human experts. While up to now convolutional neural networks have mostly been applied to light optimal microscopy and scanning electron microscope micrographs, application to EBSD micrographs will be increasingly common as rational design generates materials with unknown textures and phase compositions. This raises the question of how crystallographic orientation should be represented in such a convolutional neural network, and whether this choice has a significant effect on the network's analysis and classification accuracy. Four representations of orientation information are examined and are used with convolutional neural networks to classify five synthetic microstructures with varying textures and grain geometries. Of these, a spectral embedding of crystallographic orientations in a space that respects the crystallographic symmetries performs by far the best, even when the network is trained on small volumes of data such as could be accessible by practical experiments.

Dependence of Microstructure Classification Accuracy on Crystallographic Data Representation

TL;DR

Four representations of orientation information are examined and are used with convolutional neural networks to classify five synthetic microstructures with varying textures and grain geometries, and a spectral embedding of crystallographic orientations in a space that respects the crystallographic symmetries performs by far the best.

Abstract

Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant microstructural features more efficiently and impartially than human experts. While up to now convolutional neural networks have mostly been applied to light optimal microscopy and scanning electron microscope micrographs, application to EBSD micrographs will be increasingly common as rational design generates materials with unknown textures and phase compositions. This raises the question of how crystallographic orientation should be represented in such a convolutional neural network, and whether this choice has a significant effect on the network's analysis and classification accuracy. Four representations of orientation information are examined and are used with convolutional neural networks to classify five synthetic microstructures with varying textures and grain geometries. Of these, a spectral embedding of crystallographic orientations in a space that respects the crystallographic symmetries performs by far the best, even when the network is trained on small volumes of data such as could be accessible by practical experiments.
Paper Structure (15 sections, 2 theorems, 14 equations, 6 figures, 3 tables)

This paper contains 15 sections, 2 theorems, 14 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Microstructure Classification
  3. Crystallographic Orientation
  4. Grain Data Vector Representations
  5. Convolutional Neural Networks
  6. Invariant and Equivariant Machine Learning
  7. Summary of Results
  8. Synthetic Microstructures
  9. CNN Methodology and Results
  10. Data processing
  11. Architecture design
  12. Hyperparameter sweep
  13. Results
  14. Discussion
  15. The Spectral Embedding

Key Result

Theorem A.1

Every function $f \in L^2(G)$ has a “Fourier series,” converging in the $L^2$ sense, where the ${\mathcal{D}}^{\alpha}$ are unitary representatives of the classes of inequivalent irreducible representations of $G$, the ${\mathcal{D}}^{\alpha}_{i,j}$ are their matrix coefficients in orthonormal bases, and In other words, the functions ${\mathcal{D}}_{i,j}^{\alpha}$ form an orthonormal basis for $

Figures (6)

  • Figure 1: General pipeline for how an image is processed in the feature extraction block of a CNN.
  • Figure 2: Example grain morphologies and textures from the synthetic microstructure data set.
  • Figure 3: $512 \times 512$ slices of a synthetic material are sampled via 8 level-set intersections, creating $64$$64\times 64$ square windows from each slice. Slices of the sample are taken every 10th voxel along the z-direction, which is a rough approximation of the average ESD of the matrix. Each voxel within each window has 4 associated GVDs (FID, IPF, QP, and SEQ).
  • Figure 4: General CNN model framework used for classification.
  • Figure 5: The figure above is a visualization of the hyperparameter sweep performed over the four voxel-associated data representations. Each curve represents a single model and its hyperparameters correspond to the intersection of the curve with the vertrical axes. Curves that are closer in shape to yellow correspond to models that yield high model performance, with respect to validation accuracy, whereas purplish curves are sub-optimal. Image created using Weights and Biases wandb.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Theorem A.1: Peter–Weyl Theorem for Compact Groups
  • Lemma A.2
  • proof