Supervised Machine Learning Topological States of One-Dimensional Non-Hermitian Systems

We apply supervised machine learning to study the topological states of one-dimensional non-Hermitian systems. Unlike Hermitian systems, the winding number of such non-Hermitian systems can take half integers. We focus on a non-Hermitian model, an extension of the Su–Schrieffer–Heeger model. The non-Hermitian model maintains the chiral symmetry. We find that trained neuron networks can reproduce the topological phase diagram of our model with high accuracy. This successful reproduction goes beyond the parameter space used in the training process. Through analyzing the intermediate output of the networks, we attribute the success of the networks to their mastery of computation of the winding number. Our work may motivate further investigation on the machine learning of non-Hermitian systems.