Exploring descriptors for titanium microstructure via digital fingerprints from variational autoencoders

Microstructure is key to controlling and understanding the properties of materials, but traditional approaches to describing microstructure capture only a small number of features. We require more complete descriptors of microstructure to enable data-centric approaches to materials discovery, to allow efficient storage of microstructural data and to assist in quality control in metals processing. The concept of microstructural fingerprinting , using machine learning (ML) to develop quantitative, low-dimensional descriptors of microstructures, has recently attracted significant attention. However, it is difficult to interpret conclusions drawn by ML algorithms, which are often referred to as "black boxes". For example, convolutional neural networks (CNNs) can be trained to make predictions about a material from a set of microstructural image data, but the feature space that is learned is often used uncritically and adopted without any validation. Here we explore the use of variational autoencoders (VAEs), comprising a pair of CNNs, which can be trained to produce microstructural fingerprints in a continuous latent space. The VAE architecture also permits the reconstruction of images from fingerprints, allowing us to explore how key features of microstructure are encoded in the latent space of fingerprints. We develop a VAE architecture based on ResNet18 and train it on two classes of Ti-6Al-4V optical micrographs (bimodal and lamellar) as an example of an industrially important alloy where microstructural control is critical to performance. The latent/feature space of fingerprints learned by the VAE is explored in several ways, including by supplying interpolated and randomly perturbed fingerprints to the trained decoder and via dimensionality reduction to explore the distribution and correlation of microstructural features within the latent space of fingerprints. We demonstrate that the fingerprints generated via the trained VAE exhibit smooth, interpolable behaviour with stability to local perturbations, supporting their suitability as general purpose descriptors for microstructure. The analysis of computational results uncover that key properties of the microstructures (volume fraction and grain size) are strongly correlated with position in the encoded feature space, supporting the use of VAE fingerprints for quantitative exploration of process-structure-property relationships.