Machine learning of topological insulator and Anderson insulator in the one-dimensional extended Su-Schrieffer-Heeger chain

We study disorder effects in the extended Su-Schrieffer-Heeger (SSH) model using a convolutional neural network (CNN) trained on reduced correlation matrices (RCMs) of disorder-free systems to predict winding number phase diagrams in systems with off-diagonal and diagonal disorder. The trained CNN model generalizes to chiral-symmetry-preserving off-diagonal disorder system but fails in the presence of chiral-symmetry-breaking diagonal disorder system. Using principal component analysis (PCA) of the RCM feature space, we demonstrate that disorder-free and symmetry-preserving systems share overlapping feature manifolds, whereas symmetry-breaking disorder causes them to diverge. Inverse participation ratio (IPR) and energy spectrum analysis further demonstrate that off-diagonal disorder preserves topological edge states, whereas diagonal disorder drives a transition to an Anderson insulator. Our results show that the OOD behavior of a CNN trained on clean systems can be understood through the evolution of the RCM feature space under symmetry-preserving and symmetry-breaking disorder, with IPR and energy-spectrum analyses providing the corresponding physical interpretation.