Deep learning for the design of non-Hermitian topolectrical circuits

TL;DR: Deep learning algorithms are effective in predicting the winding of eigenvalue non-Hermitian Hamiltonians and designing non-Hermitian topolectrical circuits.

Abstract: Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we introduce several algorithms with multilayer perceptron (MLP), and convolutional neural network (CNN) in the field of deep learning, to predict the winding of eigenvalue non-Hermitian Hamiltonians. Subsequently, we use the smallest module of the periodic circuit as one unit to construct high-dimensional circuit data features. Further, we use the Dense Convolutional Network (DenseNet), a type of convolutional neural network that utilizes dense connections between layers to design a non-Hermitian topolectrical Chern circuit, as the DenseNet algorithm is more suitable for processing high-dimensional data. Our results demonstrate the effectiveness of the deep learning network in capturing the global topological characteristics of a non-Hermitian system based on training data.