Training biases in machine learning for the analytic continuation of quantum many-body Green's functions

We address the problem of analytic continuation of imaginary-frequency Green's functions, which is crucial in many-body physics, using machine learning based on a multilevel residual neural network. We specifically address potential biases that can be introduced due to the use of artificially created spectral functions that are employed to train the neural network. We also implement an uncertainty estimation of the predicted spectral function, based on Monte Carlo dropout, which allows us to identify frequency regions where the prediction might not be accurate, and we study the effect of noise, in particular also for situations where the noise level during training is different from that in the actual data. Our analysis demonstrates that this method can indeed achieve a high quality of prediction, comparable to or better than the widely used maximum entropy method, but that further improvement is currently limited by the lack of true data that can be used for training. We also benchmark our approach by applying it to the case of SrVO3, where an accurate spectral function has been obtained from dynamical mean-field theory using a solver that works directly on the real frequency axis.

Automated summary

In this study, we address the problem of analytic continuation of imaginary-frequency Green's functions in many-body physics. We use a machine learning approach based on a multilevel residual neural network and consider potential biases introduced by training the network on artificially created spectral functions. We also implement an uncertainty estimation of the predicted spectral function and study the effect of noise during training. Our analysis shows that this method can achieve high-quality predictions comparable to or better than the widely used maximum entropy method, but further improvement is limited by the lack of true training data.