Noise Enhanced Neural Networks for Analytic Continuation

Abstract

Analytic continuation maps imaginary-time Green's functions obtained by various theoretical/numerical methods to real-time response functions that can be directly compared with experiments. Analytic continuation is an important bridge between many-body theories and experiments but is also a challenging problem because such mappings are ill-conditioned. In this work, we develop a neural network-based method for this problem. The training data is generated either using synthetic Gaussian-type spectral functions or from exactly solvable models where the analytic continuation can be obtained analytically. Then, we applied the trained neural network to the testing data, either with synthetic noise or intrinsic noise in Monte Carlo simulations. We conclude that the best performance is always achieved when a proper amount of noise is added to the training data. Moreover, our method can successfully capture multi-peak structure in the resulting response function for the cases with the best performance. The method can be combined with Monte Carlo simulations to compare with experiments on real-time dynamics.

Progress on stochastic analytic continuation of quantum Monte Carlo data

“…The neural network is trained to deliver S(ω) given G(τ ) (with noise if appropriate for the intended application). These methods show some promise, e.g., it was claimed that they can resolve a Gaussian peak better than the ME method [35], and examples of spectra with sharp-edged features have also been presented [100]. However, mostly what has been produced so far can also be achieved with standard ME or SAC methods, and much better results can likely be produced with the improved methods developed here.…”

“…Machine learning (ML) methods are making inroads on many fronts in quantum many-body physics, including applications to the analytic continuation problem [34,35,[98][99][100]. Without going into details, the attempts so far use a large data set of known spectral functions S(ω) and their associated imaginary-time correlation function G(τ ).…”