# Towards Microstructural State Variables in Materials Systems

arXiv: https://arxiv.org/abs/2301.04261 · HTML: https://mlsanity.com/paper/2301.04261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Learning disentangled representations via product manifold projection](https://mlsanity.com/paper/2103.01638/) (2021)
- [Inferring low-dimensional microstructure representations using convolutional neural networks](https://mlsanity.com/paper/1611.02764/) (2016)
- [Microstructure synthesis using style-based generative adversarial network](https://mlsanity.com/paper/1909.07042/) (2019)

## Abstract (arXiv)

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.