HOLISMOKES XXI: Detecting strongly lensed type Ia supernovae from time series of multi-band LSST-like imaging data -- Part II
Strong gravitationally lensed supernovae (LSNe) are rare but extremely valuable probes of cosmology and astrophysics. Prompt identification within the alert streams of time-domain surveys such as the Rubin Legacy Survey of Space and Time (LSST) is essential for timely follow-up observations. In our previous study, Bag et al. (2026), we introduced a deep-learning framework for detecting LSNe Ia directly from multi-band, multi-epoch image cutouts. The model employs a convolutional LSTM architecture to capture spatiotemporal correlations in time-series imaging data, enabling classification updates as new observations arrive. In this work, we extend that framework by incorporating greater realism into the simulations. In particular, we present a method to construct realistic image time series from single-epoch observations by introducing epoch-to-epoch point spread function variations with corresponding variance-map corrections. The dataset is based on HSC PDR3 observations and includes simulated lensed host-galaxy arcs, SN light-curve variations, and Poisson noise. We also introduce an additional negative class consisting of SN Ia occurring in the foreground lens galaxy, representing a challenging source of false positives. Despite these additional complexities, the model retains strong performance. The receiver operating characteristic improves rapidly during the first few observations, reaching a true-positive rate of $\sim60\%$ at a false-positive rate of $\mathcal{O}(10^{-4})$ by the seventh observation and $\sim80\%$ by the tenth. We also investigate potential confusion with sibling SNe occurring in LRGs and identify the configurations that best mimic lensed systems. These results demonstrate that the image-time-series approach remains robust under more realistic observing conditions, and is well suited for real-time LSN searches in LSST and other time-domain surveys.