Artificial Neural Network Approach to the Analytic Continuation Problem.

Area of Science:

• Physics
• Computational Physics
• Machine Learning

Background:

• Analytic continuation of imaginary Green's functions to the real frequency domain is crucial in physics.
• This problem is ill-posed, lacking known analytic solutions.
• Existing methods like maximum entropy can be computationally expensive and sensitive to noise.

Purpose of the Study:

• To present a general framework for an artificial neural network (ANN) to solve the analytic continuation problem.
• To demonstrate the ANN's accuracy and efficiency compared to established methods.
• To provide a computationally cheaper and more robust alternative for Green's function analysis.

Main Methods:

• Developed a supervised learning framework using artificial neural networks (ANNs).
• Applied the ANN to quantum Monte Carlo calculations and simulated Green's function data.
• Compared ANN performance against the maximum entropy method.

Main Results:

• The ANN approach demonstrated high accuracy in analytic continuation.
• The ANN achieved comparable accuracy to the maximum entropy method for low-noise data.
• The ANN significantly outperformed the maximum entropy method with increasing noise levels.
• The ANN method reduced computational cost by nearly three orders of magnitude.

Conclusions:

• Artificial neural networks offer a powerful and efficient solution for the analytic continuation of Green's functions.
• The proposed ANN method is more robust to noise and computationally less demanding than the maximum entropy method.
• This work provides a significant advancement in solving inverse problems in computational physics.