  We have updated and applied a convolutional neural network (CNN) machine
learning model to discover and characterize damped Ly$\alpha$ systems (DLAs)
based on Dark Energy Spectroscopic Instrument (DESI) mock spectra. We have
optimized the training process and constructed a CNN model that yields a DLA
classification accuracy above 99$\%$ for spectra which have signal-to-noise
(S/N) above 5 per pixel. Classification accuracy is the rate of correct
classifications. This accuracy remains above 97$\%$ for lower signal-to-noise
(S/N) $\approx1$ spectra. This CNN model provides estimations for redshift and
HI column density with standard deviations of 0.002 and 0.17 dex for spectra
with S/N above 3 per pixel. Also, this DLA finder is able to identify
overlapping DLAs and sub-DLAs. Further, the impact of different DLA catalogs on
the measurement of Baryon Acoustic Oscillation (BAO) is investigated. The
cosmological fitting parameter result for BAO has less than $0.61\%$ difference
compared to analysis of the mock results with perfect knowledge of DLAs. This
difference is lower than the statistical error for the first year estimated
from the mock spectra: above $1.7\%$. We also compared the performance of CNN
and Gaussian Process (GP) model. Our improved CNN model has moderately 14$\%$
higher purity and 7$\%$ higher completeness than an older version of GP code,
for S/N $>$ 3. Both codes provide good DLA redshift estimates, but the GP
produces a better column density estimate by $24\%$ less standard deviation. A
credible DLA catalog for DESI main survey can be provided by combining these
two algorithms.
