Analytic Continuation by Feature Learning

TL;DR

This paper introduces FL-net, a neural network architecture that significantly improves the accuracy of analytic continuation for spectral functions, offering insights into robustness and model design.

Contribution

We propose a novel neural network, FL-net, that outperforms traditional and previous neural methods in analytic continuation tasks, and develop an analytical robustness evaluation method.

Findings

FL-net achieves at least 20% better accuracy than traditional methods.

Increasing hidden dimensionality reduces robustness despite lower loss.

The model provides insights into the trade-off between accuracy and robustness.

Abstract

Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the Feature Learning Network (FL-net), to enhance the prediction accuracy of spectral functions, achieving an improvement of at least $20\%$ over traditional methods, such as the Maximum Entropy Method (MEM), and previous neural network approaches. Furthermore, we develop an analytical method to evaluate the robustness of the proposed network. Using this method, we demonstrate that increasing the hidden dimensionality of FL-net, while leading to lower loss, results in decreased robustness. Overall, our model provides valuable insights into effectively addressing the complex challenges associated with analytic continuation.