  Galaxy rotation curve (RC) fitting is an important technique which allows the
placement of constraints on different kinds of dark matter (DM) halo models. In
the case of non-phenomenological DM profiles with no analytic expressions, the
art of finding RC best-fits including the full baryonic $+$ DM free parameters
can be difficult and time-consuming. In the present work, we use a gradient
descent method used in the backpropagation process of training a neural
network, to fit the so-called Grand Rotation Curve of the Milky Way (MW)
ranging from $\sim$1 pc all the way to $\sim$$10^5$ pc. We model the mass
distribution of our Galaxy including a bulge (inner $+$ main), a disk, and a
fermionic dark matter (DM) halo known as the Ruffini-Arg\"uelles-Rueda (RAR)
model. This is a semi-analytical model built from first-principle physics such
as (quantum) statistical mechanics and thermodynamics, whose more general
density profile has a dense core -- diluted halo morphology with no analytic
expression. As shown recently and further verified here, the dark and compact
fermion-core can work as an alternative to the central black hole in SgrA* when
including data at milliparsec scales from the S-cluster stars. Thus, we show
the ability of this state-of-the-art machine learning tool in providing the
best-fit parameters to the overall MW RC in the $10^{-2}$--$10^5$ pc range, in
a few hours of CPU time.
