  We construct and train an artificial neural network called the
back-propagation neural network to describe the evolution of the type Ia
supernova spectrum by using the data from the CfA Supernova Program. This
network method has many attractive features, and one of them is that the
constructed model is differentiable. Benefitting from this, we calculate the
absorption velocity and its variation. The model we constructed can well
describe not only the spectrum of SNe Ia with wavelength range from $3500\AA$
to $8000\AA$, but also the light-curve evolution with phase time from $-15$ to
$50$ with different colors. Moreover, the number of parameters needed during
the training process is much less than the usual methods.
