Neural network approach to reconstructing spectral functions and complex poles of confined particles

TL;DR

This paper introduces a neural network method for reconstructing spectral functions and complex poles from propagator data, demonstrating improved accuracy and robustness on toy and lattice QCD data.

Contribution

It extends previous neural network approaches by also reconstructing complex poles and IR cutoffs, enhancing the analysis of confined particles.

Findings

Neural network accurately reconstructs spectral functions from noisy data.

Method successfully applies to lattice QCD gluon propagator data.

Reconstruction shows potential for significant improvements over existing methods.

Abstract

Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to solve this problem and has shown promising results, either matching or improving upon the performance of other methods. We generalize this approach by not only reconstructing spectral functions, but also (possible) pairs of complex poles or an infrared (IR) cutoff. We train our network on physically motivated toy functions, examine the reconstruction accuracy and check its robustness to noise. Encouraging results are found on both toy functions and genuine lattice QCD data for the gluon propagator, suggesting that this approach may lead to significant improvements over current state-of-the-art methods.