Prediction of impurity spectrum function by deep learning algorithm

Abstract

By using the numerical renormalization group (NRG) method, we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model. The dataset contains the density of states (DOS) of the host material, the strength of Coulomb interaction between on-site electrons (U), and the hybridization between the host material and the impurity site (Γ). The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions, respectively. From this dataset, we build seven different machine learning networks to predict the spectral function from the input data, DOS, U, and Γ. Three different evaluation indexes, mean absolute error (MAE), relative error (RE) and root mean square error (RMSE), are used to analyze the prediction abilities of different network models. Detailed analysis shows that, for the two kinds of widely used recurrent neural networks (RNNs), gate recurrent unit (GRU) has better performance than the long short term memory (LSTM) network. A combination of bidirectional GRU (BiGRU) and GRU has the best performance among GRU, BiGRU, LSTM, and BiLSTM. The MAE peak of BiGRU+GRU reaches 0.00037. We have also tested a one-dimensional convolutional neural network (1DCNN) with 20 hidden layers and a residual neural network (ResNet), we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset, while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets. The ResNet has the worst performance among all the seven network models. The datasets presented in this paper, including the large data set of the spectral function of Anderson quantum impurity model, are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.