The studies of topological phases and energy braiding of non-Hermitian models using machine learning

Abstract Complex-energy bands in non-Hermitian systems can exhibit diverse topological braiding, yet identifying these braids remains challenging and has garnered limited attention in previous studies. In this work, we explore energy braiding in one-dimensional non-Hermitian systems through both unsupervised and supervised learning techniques. For unsupervised learning, we apply diffusion maps to effectively identify non-Bloch energy braiding without requiring prior knowledge and use k-means clustering to categorize different topological features, such as Unlink and Hopf link configurations. In the supervised learning phase, we train a Convolutional Neural Network (CNN) on Bloch energy data to predict both Bloch and non-Bloch energy braiding with nearly 100% accuracy. Through an analysis of the CNN, we confirm that the model has successfully developed the capacity to recognize the braiding topology of the energy bands. Our findings reveal that unsupervised learning can rapidly detect phase transition points, while the CNN is capable of predicting braid degrees even for models not included in the training set.