Artificial neural network for constructing type Ia supernovae spectrum evolution model

We construct and train an artificial neural network called the backpropagation 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. Benefiting 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 Å to 8000 Å 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.

Figure 1

Typical structure of an ANN.

Figure 2

Number distributions of the spectra and SN Ia.

Figure 3

Redshift distribution of the spectra.

Figure 4

Parameter distribution of the spectra.

Figure 5

The RMSE and MAE vs the neuron number in the hidden level for the BPNN with only one hidden level.

Figure 6

Three-dimensional vision: A best-trained spectrum evolution model.

Figure 7

Contour: A best-trained spectrum evolution model.

Figure 8

Evolution of spectrum with phase, where the number in parentheses denotes the phase.

Figure 9

Color vs phase.

Figure 10

Comparison of different color spectra. The black dashed line is SALT2 template spectra.

Figure 11

Evolution of the Si II $\lambda 6355$ absorption velocity with time for the spectra of different colors.

Figure 12

$\partial V_{\mathrm{abs}}/\partial t$ as a function of phase.