  Stellar abundances for a large number of stars are key information for the
study of Galactic formation history. Large spectroscopic surveys such as DESI
and LAMOST take median-to-low resolution ($R\lesssim5000$) spectra in the full
optical wavelength range for millions of stars. However, line blending effect
in these spectra causes great challenges for the elemental abundances
determination. Here we employ the DD-PAYNE, a data-driven method regularised by
differential spectra from stellar physical models, to the DESI EDR spectra for
stellar abundance determination. Our implementation delivers 15 labels,
including effective temperature $T_{\rm eff}$, surface gravity $\log g$,
microturbulence velocity $v_{\rm mic}$, and abundances for 12 individual
elements, namely C, N, O, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, Ni. Given a spectral
signal-to-noise ratio of 100 per pixel, internal precision of the label
estimates are about 20 K for $T_{\rm eff}$, 0.05 dex for $\log~g$, and 0.05 dex
for most elemental abundances. These results are agree with theoretical limits
from the Cr\'amer-Rao bound calculation within a factor of two. The
Gaia-Enceladus-Sausage that contributes the majority of the accreted halo stars
are discernible from the disk and in-situ halo populations in the resultant
[Mg/Fe]-[Fe/H] and [Al/Fe]-[Fe/H] abundance spaces. We also provide distance
and orbital parameters for the sample stars, which spread a distance out to
$\sim$100 kpc. The DESI sample has a significant higher fraction of distant (or
metal-poor) stars than other existed spectroscopic surveys, making it a
powerful data set to study the Galactic outskirts. The catalog is publicly
available.
