Pole-fitting for complex functions: enhancing standard techniques by artificial-neural-network classifiers and regressors

TL;DR

This paper compares traditional, neural network, and combined methods for accurately identifying pole positions of complex functions from limited real-axis data, with applications in theoretical physics.

Contribution

It introduces a hybrid approach combining standard algorithms and neural networks for efficient pole fitting, improving reliability and speed over existing methods.

Findings

The combined method outperforms individual techniques in accuracy.

Neural networks enhance pole detection efficiency.

Approach is applicable to similar complex analysis problems.

Abstract

Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the singularities closest to the origin for a function that is only known numerically on a specific finite grid of values on the positive real axis. For this problem, we compare the efficiency of standard techniques, like the Levenberg-Marquardt algorithm, to a pure artificial-neural-network approach as well as a combination of these two. This combination is more efficient than any of the two techniques separately. Such an approach is generalizable to similar situations, where the positions of poles of a function in a complex variable must be quickly and reliably estimated from real-axis information alone.