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.

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• Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions
• Stochastic pole expansion method
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Neural Network Analytic Continuation for Monte Carlo: Improvement by Statistical Errors
• Autoencoder-based analytic continuation method for strongly correlated quantum systems