Artificial neural network for constructing type Ia supernovae spectrum evolution model

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.