HOLISMOKES: XII. Time-delay measurements of strongly lensed Type Ia supernovae using a long short-term memory network

Strongly lensed Type Ia supernovae (LSNe Ia) are a promising probe with which to measure the Hubble constant (H0) directly. To use LSNe Ia for cosmography, a time-delay measurement between multiple images, a lens-mass model, and a mass reconstruction along the line of sight are required. In this work, we present the machine-learning network LSTM-FCNN, which is a combination of a long short-term memory network (LSTM) and a fully connected neural network (FCNN). The LSTM-FCNN is designed to measure time delays on a sample of LSNe Ia spanning a broad range of properties, which we expect to find with the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) and for which follow-up observations are planned. With follow-up observations in the i band (cadence of one to three days with a single-epoch 5σ depth of 24.5 mag), we reach a bias-free delay measurement with a precision of around 0.7 days over a large sample of LSNe Ia. The LSTM-FCNN is far more general than previous machine-learning approaches such as the random forest (RF) one, whereby an RF has to be trained for each observational pattern separately, and yet the LSTM-FCNN outperforms the RF by a factor of roughly three. Therefore, the LSTM-FCNN is a very promising approach to achieve robust time delays in LSNe Ia, which is important for a precise and accurate constraint on H0.