Artificial Neural Network Approach to the Analytic Continuation Problem

TL;DR

This paper introduces a neural network framework for the ill-posed analytic continuation problem in physics, demonstrating high accuracy and efficiency, especially with noisy data, outperforming traditional methods.

Contribution

The authors develop a supervised neural network approach for analytic continuation, providing a fast, accurate alternative to maximum entropy methods, particularly in high-noise scenarios.

Findings

Neural network achieves comparable accuracy to maximum entropy for low-noise data.

Performance significantly surpasses maximum entropy with increased noise.

Computational cost is reduced by nearly three orders of magnitude.

Abstract

Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method