Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Toward Learning Latent-Variable Representations of Microstructures by Optimizing in Spatial Statistics Space

Sayed Sajad Hashemi, Michael Guerzhoy, Noah H. Paulson

TL;DR

The paper addresses the challenge of obtaining low-dimensional representations of stochastic microstructures for materials design by training a variational autoencoder to preserve spatial statistics rather than exact pixel values. It introduces a differentiable spatial-statistics loss, $L = \alpha \\cdot ||f(\\boldsymbol{x}) - f(\\boldsymbol{x}_{recon})||_2 + \beta \\cdot \text{Loss}_{KL}$, and optimizes the VAE to minimize this distance in spatial statistics space, leveraging a differentiable FFT-based computation of auto-correlations. Empirically, the method yields reconstructions that align more closely with the original in spatial statistics than a data-space baseline, demonstrated on a large texture dataset with quantitative metrics such as orientation and line-count preservation, and volume-fraction differences. This approach enables compact latent representations that retain texture information, offering a pathway for rapid exploration and design of microstructures in materials science.

Abstract

In Materials Science, material development involves evaluating and optimizing the internal structures of the material, generically referred to as microstructures. Microstructures structure is stochastic, analogously to image textures. A particular microstructure can be well characterized by its spatial statistics, analogously to image texture being characterized by the response to a Fourier-like filter bank. Material design would benefit from low-dimensional representation of microstructures Paulson et al. (2017). In this work, we train a Variational Autoencoders (VAE) to produce reconstructions of textures that preserve the spatial statistics of the original texture, while not necessarily reconstructing the same image in data space. We accomplish this by adding a differentiable term to the cost function in order to minimize the distance between the original and the reconstruction in spatial statistics space. Our experiments indicate that it is possible to train a VAE that minimizes the distance in spatial statistics space between the original and the reconstruction of synthetic images. In future work, we will apply the same techniques to microstructures, with the goal of obtaining low-dimensional representations of material microstructures.

Toward Learning Latent-Variable Representations of Microstructures by Optimizing in Spatial Statistics Space

TL;DR

The paper addresses the challenge of obtaining low-dimensional representations of stochastic microstructures for materials design by training a variational autoencoder to preserve spatial statistics rather than exact pixel values. It introduces a differentiable spatial-statistics loss, , and optimizes the VAE to minimize this distance in spatial statistics space, leveraging a differentiable FFT-based computation of auto-correlations. Empirically, the method yields reconstructions that align more closely with the original in spatial statistics than a data-space baseline, demonstrated on a large texture dataset with quantitative metrics such as orientation and line-count preservation, and volume-fraction differences. This approach enables compact latent representations that retain texture information, offering a pathway for rapid exploration and design of microstructures in materials science.

Abstract

In Materials Science, material development involves evaluating and optimizing the internal structures of the material, generically referred to as microstructures. Microstructures structure is stochastic, analogously to image textures. A particular microstructure can be well characterized by its spatial statistics, analogously to image texture being characterized by the response to a Fourier-like filter bank. Material design would benefit from low-dimensional representation of microstructures Paulson et al. (2017). In this work, we train a Variational Autoencoders (VAE) to produce reconstructions of textures that preserve the spatial statistics of the original texture, while not necessarily reconstructing the same image in data space. We accomplish this by adding a differentiable term to the cost function in order to minimize the distance between the original and the reconstruction in spatial statistics space. Our experiments indicate that it is possible to train a VAE that minimizes the distance in spatial statistics space between the original and the reconstruction of synthetic images. In future work, we will apply the same techniques to microstructures, with the goal of obtaining low-dimensional representations of material microstructures.
Paper Structure (13 sections, 2 equations, 4 figures, 6 tables)

This paper contains 13 sections, 2 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Methods
  4. Results
  5. Experimental Setup
  6. Evaluation
  7. Calculation of volume fraction difference
  8. Image thresholding function
  9. Number of lines in original images vs. reconstructions
  10. Quantitative results for original VAE and our VAE
  11. More illustrative examples
  12. Reconstructions and their spatial statistics
  13. Reconstructions along with most similar images from the training set

Figures (4)

  • Figure 1: The VAE with spatial statistics loss.
  • Figure 2: The difference between percentage of black pixels in the input image and the percentage of black pixels in the reconstruction.
  • Figure 3: Line count in the reconstructed image vs original image (left), line count in image closes in spatial statistics space vs line in count in original image (right)
  • Figure :