  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.
