Cosmologists are facing the problem of the analysis of a huge quantity of data when observing the sky. The methods used in cos-mology are, for the most of them, relying on astrophysical models, and thus, for the classification, they usually use a machine learning approach in two-steps, which consists in, first, extracting features , and second, using a classifier. In this paper, we are specifically studying the supernovae phenomenon and especially the binary classification "I.a supernovae versus not-I.a supernovae". We present two Convolutional Neural Networks (CNNs) defeating the current state-of-the-art. The first one is adapted to time series and thus to the treatment of supernovae light-curves. The second one is based on a Siamese CNN and is suited to the nature of data, i.e. their sparsity and their weak quantity (small learning database).