  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.
