Detecting unresolved lensed SNe Ia in LSST using blended light curves

Strongly gravitationally lensed supernovae (LSNe) are promising probes for providing absolute distance measurements using gravitational-lens time delays. Spatially unresolved LSNe offer an opportunity to enhance the sample size for precision cosmology. We predict that there will be approximately three times as many unresolved as resolved LSNe Ia in the Legacy Survey of Space and Time (LSST) by the {\it Rubin} Observatory. In this article, we explore the feasibility of detecting unresolved LSNe Ia from a pool of preclassified SNe Ia light curves using the shape of the blended light curves with deep-learning techniques. We find that $\sim 30\%$ unresolved LSNe Ia can be detected with a simple 1D convolutional neural network (CNN) using well-sampled $rizy$-band light curves (with a false-positive rate of $\sim 3\%$). Even when the light curve is well observed in only a single band among $r$, $i$, and $z$, detection is still possible with false-positive rates ranging from $\sim 4$ to $7\%$ depending on the band. Furthermore, we demonstrate that these unresolved cases can be detected at an early stage using light curves up to $\sim20$ days from the first observation with well-controlled false-positive rates, providing ample opportunity to trigger follow-up observations. Additionally, we demonstrate the feasibility of time-delay estimations using solely LSST-like data of unresolved light curves, particularly for doubles, when excluding systems with low time delays and magnification ratios. However, the abundance of such systems among those unresolved in LSST poses a significant challenge. This approach holds potential utility for upcoming wide-field surveys, and overall results could significantly improve with enhanced cadence and depth in the future surveys.