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

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.

Automated summary

Motivated by a use case in theoretical hadron physics, this paper revisits an application of a pole-sum fit to dressing functions of a confined quark propagator. Specifically, it investigates approaches to determine the number and positions of singularities closest to the origin for a function known numerically on a specific grid on the positive real axis. Comparing the efficiency of standard techniques to a pure artificial-neural-network approach and a combination of both, it finds that the combined approach is more efficient. This approach can be applied to similar situations where the positions of poles need to be estimated quickly and reliably from real-axis information alone.