Machine-Learning Characterization of Coarsening Dynamics in Fingerprint Labyrinthine Patterns

Labyrinthine patterns are disordered spatial structures that emerge in homogeneous media, exhibiting short-range order without long-range orientational coherence. Following a thermal quench, transient configurations fail to develop global order and instead evolve into glassy states characterized by slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned by an effective periodic potential induced by the intrinsic periodicity of the stripe pattern. The Turing-Swift-Hohenberg (TSH) model displays a rich variety of such labyrinthine morphologies as the bifurcation parameter increases. Here we employ modern machine-learning techniques to characterize the coarsening dynamics of labyrinthine phases with fingerprint-like stripe patterns, complementing traditional Fourier-based analyses. In particular, we introduce a template-matching convolutional neural network framework to detect and classify point-like defects in the local stripe order. By tracking the temporal evolution of spatial correlations and defect geometries, we uncover new aspects of the slow relaxation and defect-mediated coarsening dynamics in labyrinthine pattern formation.