HOLISMOKES -- VII. Time-delay measurement of strongly lensed Type Ia
  supernovae using machine learning
  The Hubble constant ($H_0$) is one of the fundamental parameters in
cosmology, but there is a heated debate around the $>$4$\sigma$ tension between
the local Cepheid distance ladder and the early Universe measurements. Strongly
lensed Type Ia supernovae (LSNe Ia) are an independent and direct way to
measure $H_0$, where a time-delay measurement between the multiple supernova
(SN) images is required. In this work, we present two machine learning
approaches for measuring time delays in LSNe Ia, namely, a fully connected
neural network (FCNN) and a random forest (RF). For the training of the FCNN
and the RF, we simulate mock LSNe Ia from theoretical SN Ia models that include
observational noise and microlensing. We test the generalizability of the
machine learning models by using a final test set based on empirical LSN Ia
light curves not used in the training process, and we find that only the RF
provides a low enough bias to achieve precision cosmology; as such, RF is
therefore preferred over our FCNN approach for applications to real systems.
For the RF with single-band photometry in the $i$ band, we obtain an accuracy
better than 1\% in all investigated cases for time delays longer than 15 days,
assuming follow-up observations with a 5$\sigma$ point-source depth of 24.7, a
two day cadence with a few random gaps, and a detection of the LSNe Ia 8 to 10
days before peak in the observer frame. In terms of precision, we can achieve
an approximately 1.5-day uncertainty for a typical source redshift of $\sim$0.8
on the $i$ band under the same assumptions. To improve the measurement, we find
that using three bands, where we train a RF for each band separately and
combine them afterward, helps to reduce the uncertainty to $\sim$1.0 day. We
have publicly released the microlensed spectra and light curves used in this
work.
