Predicting impurity spectral functions using machine learning

TL;DR

This paper demonstrates that neural networks can accurately and efficiently predict impurity spectral functions across all regimes of the Anderson Impurity Model, significantly outperforming traditional methods.

Contribution

The study introduces large spectral databases and shows neural networks outperform kernel ridge regression in predicting AIM spectral functions, with substantial speedups.

Findings

Neural networks achieve mean absolute errors as low as 0.003.

NN models outperform KRR models in accuracy.

Speedup of approximately 10^5 over traditional AIM solvers.

Abstract

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410k and 600k spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with point-wise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of $10^5$ over traditional AIM solvers. The required size of the training set of our model can be significantly reduced using furthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multi-channel impurity problems of relevance to predicting the properties of real materials.