Machine learning classification of dynamical phases in a driven nonlinear Su-Schrieffer-Heeger lattice

Abstract

Driven nonlinear photonic lattices can settle into steady, symmetry-broken, periodic, or chaotic states, and mapping where each occurs in parameter space is key to device design. Brute-force mapping is slow and relies on hand-built criteria, while machine-learning classifiers are usually tested on different systems, so it is unclear which suits a new lattice. We therefore apply four classifiers to the same coherently driven Su-Schrieffer-Heeger (SSH) chain of Kerr resonators: a hand-built heuristic classifier based on Lyapunov exponents and spectral diagnostics, a supervised convolutional neural network (CNN) trained on the heuristic labels, an unsupervised library-building scheme based on augmented dynamic mode decomposition (aDMD), and an unsupervised Gaussian mixture model (GMM) on four dynamical invariants that include an aDMD reconstruction error. Using a converged heuristic diagram as the reference, the CNN reaches 98.0% held-out accuracy, while the two label-free methods reach adjusted Rand indices (ARIs) of 0.916 and 0.947, respectively, without seeing any labels. We show that the aDMD library cleanly resolves the stable and bistable phases and separates symmetric from symmetry-broken periodic oscillations, which the heuristic misses, though it cannot distinguish periodic from chaotic switching. We also find that a poorly converged reference understates the label-free methods' accuracy.