  Obtaining high-quality magnetic and velocity fields through Stokes inversion
is crucial in solar physics. In this paper, we present a new deep learning
method, named Stacked Deep Neural Networks (SDNN), for inferring line-of-sight
(LOS) velocities and Doppler widths from Stokes profiles collected by the Near
InfraRed Imaging Spectropolarimeter (NIRIS) on the 1.6 m Goode Solar Telescope
(GST) at the Big Bear Solar Observatory (BBSO). The training data of SDNN is
prepared by a Milne-Eddington (ME) inversion code used by BBSO. We
quantitatively assess SDNN, comparing its inversion results with those obtained
by the ME inversion code and related machine learning (ML) algorithms such as
multiple support vector regression, multilayer perceptrons and a pixel-level
convolutional neural network. Major findings from our experimental study are
summarized as follows. First, the SDNN-inferred LOS velocities are highly
correlated to the ME-calculated ones with the Pearson product-moment
correlation coefficient being close to 0.9 on average. Second, SDNN is faster,
while producing smoother and cleaner LOS velocity and Doppler width maps, than
the ME inversion code. Third, the maps produced by SDNN are closer to ME's maps
than those from the related ML algorithms, demonstrating the better learning
capability of SDNN than the ML algorithms. Finally, comparison between the
inversion results of ME and SDNN based on GST/NIRIS and those from the
Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory in
flare-prolific active region NOAA 12673 is presented. We also discuss
extensions of SDNN for inferring vector magnetic fields with empirical
evaluation.
