deepSIP: linking Type Ia supernova spectra to photometric quantities with deep learning

We present deepSIP (deep learning of Supernova Ia Parameters), a software package for measuring the phase and - for the first time using deep learning - the light-curve shape of a Type Ia supernova (SN Ia) from an optical spectrum. At its core, deepSIP consists of three convolutional neural networks trained on a substantial fraction of all publicly available low-redshift SN Ia optical spectra, on to which we have carefully coupled photometrically derived quantities. We describe the accumulation of our spectroscopic and photometric data sets, the cuts taken to ensure quality, and our standardized technique for fitting light curves. These considerations yield a compilation of 2754 spectra with photometrically characterized phases and light-curve shapes. Though such a sample is significant in the SN community, it is small by deep-learning standards where networks routinely have millions or even billions of free parameters. We therefore introduce a data-augmentation strategy that meaningfully increases the size of the subset we allocate for training while prioritizing model robustness and telescope agnosticism. We demonstrate the effectiveness of our models by deploying them on a sample unseen during training and hyperparameter selection, finding that Model I identifies spectra that have a phase between -10 and 18 d and light-curve shape, parametrized by Δm₁₅, between 0.85 and 1.55 mag with an accuracy of 94.6 per cent. For those spectra that do fall within the aforementioned region in phase-Δm₁₅ space, Model II predicts phases with a root-mean-square error (RMSE) of 1.00 d and Model III predicts Δm₁₅ values with an RMSE of 0.068 mag.