Coarsening dynamics of fingerprint labyrinthine patterns: Machine learning assisted characterization

Abstract

Fingerprint labyrinthine patterns exhibit a level of structural complexity beyond simple stripe phases, combining local stripe order with a dense network of point-like defects. Unlike symmetry-breaking phases, where coarsening proceeds via diffusive defect annihilation, or conventional stripe phases, where curvature-driven motion of extended grain boundaries dominates, the coarsening of fingerprint labyrinths is governed primarily by localized junction and terminal defects. Using the Turing-Swift-Hohenberg equation, we study the nonequilibrium relaxation of fingerprint labyrinthine patterns following a quench. To go beyond conventional Fourier-based diagnostics, we employ a template-matching convolutional neural network (TM-CNN) to identify and track junctions and terminals directly in real space, enabling a quantitative characterization of defect statistics and spatial correlations. We show that, although these point-like defects drive coarsening, their motion is strongly constrained by the surrounding stripe geometry, leading to slow, nondiffusive dynamics that are qualitatively distinct from both conventional phase ordering and stripe coarsening. Together, these results establish defect-mediated dynamics as the central organizing principle of fingerprint labyrinthine coarsening and demonstrate the effectiveness of machine-learning-assisted approaches for complex pattern-forming systems.