Interpretable liquid crystal phase classification via two-by-two ordinal patterns

TL;DR

This paper introduces an interpretable 75-dimensional ordinal pattern frequency representation combined with a simple classifier for accurate liquid crystal phase identification, including challenging distinctions, with explanations revealing texture determinants.

Contribution

It presents a novel, interpretable ordinal pattern-based method for liquid crystal phase classification that outperforms deep learning in interpretability and generalizes well to unseen compounds.

Findings

Near-perfect phase recognition accuracy achieved.

Effectively distinguishes between smectic A and B phases.

Model explanations reveal texture determinants and pattern interactions.

Abstract

Liquid crystal textures encode rich structural information, yet mapping these images to mesophase identity remains challenging because visually similar patterns can arise from distinct structures. Here we present a simple, interpretable representation that maps textures to a 75-dimensional frequency vector of two-by-two ordinal patterns, grouped into eleven symmetry-based types to characterize a large-scale dataset spanning seven mesophases. Combined with a simple machine learning classifier, this lightweight representation yields near-perfect phase recognition, including the difficult distinction between smectic A and smectic B mesophases. Our approach generalizes to unseen compounds and accurately distinguishes between phase identity and material origin. Unlike deep learning methods, each ordinal pattern is readily interpretable, and model explanations augmented with network visualizations of pattern interactions reveal the specific types and pairwise dependencies that drive each mesophase decision, providing compact, physically meaningful summaries of texture determinants. These results establish two-by-two ordinal patterns as an interpretable and scalable tool for liquid crystal image analysis, with potential applications to other complex patterned systems in materials science.