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

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.

16 two-column pages, 8 figures, supplementary information; accepted for publication in Physical Review E

References in corpus (17)

• XGBoost: A Scalable Tree Boosting System
• scikit-image: Image processing in Python
• Machine learning and the physical sciences
• Searching for Exotic Particles in High-Energy Physics with Deep Learning
• Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns
• ordpy: A Python package for data analysis with permutation entropy and ordinal network methods
• Deep-Learning continuous gravitational waves
• Transient Classification in LIGO data using Difference Boosting Neural Network
• Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane
• Learning physical properties of liquid crystals with deep convolutional neural networks
• Estimating physical properties from liquid crystal textures via machine learning and complexity-entropy methods
• Determining liquid crystal properties with ordinal networks and machine learning
• Mapping images into ordinal networks
• Two new parameters for the ordinal analysis of images
• Detection of Islands and Droplets on Smectic Films Using Machine Learning
• Characterizing unstructured data with the nearest neighbor permutation entropy
• Two-by-two ordinal patterns in art paintings