Machine learning topological energy braiding of non-Bloch bands

Abstract: Machine learning has been used to identify phase transitions in a variety of physical systems. However, there is still a lack of relevant research on non-Bloch energy braiding in non-Hermitian systems. In this work, we study non-Bloch energy braiding in one-dimensional non-Hermitian systems using unsupervised and supervised methods. In unsupervised learning, we use diffusion maps to successfully identify non-Bloch energy braiding without any prior knowledge and combine it with k-means to cluster different topological elements into clusters, such as Unlink and Hopf link. In supervised learning, we train a Convolutional Neural Network (CNN) based on Bloch energy data to predict not only Bloch energy braiding but also non-Bloch energy braiding with an accuracy approaching 100%. By analysing the CNN, we can ascertain that the network has successfully acquired the ability to recognise the braiding topology of the energy bands. The present study demonstrates the considerable potential of machine learning in the identification of non-Hermitian topological phases and energy braiding.