Inferring the Hubble Constant Using Simulated Strongly Lensed Supernovae and Neural Network Ensembles

Strongly lensed supernovae are a promising new probe to obtain independent measurements of the Hubble constant (${H_0}$). In this work, we employ simulated gravitationally lensed Type Ia supernovae (glSNe Ia) to train our machine learning (ML) pipeline to constrain $H_0$. We simulate image time-series of glSNIa, as observed with the upcoming Nancy Grace Roman Space Telescope, that we employ for training an ensemble of five convolutional neural networks (CNNs). The outputs of this ensemble network are combined with a simulation-based inference (SBI) framework to quantify the uncertainties on the network predictions and infer full posteriors for the $H_0$ estimates. We illustrate that the combination of multiple glSN systems enhances constraint precision, providing a $4.4\%$ estimate of $H_0$ based on 100 simulated systems, which is in agreement with the ground truth. This research highlights the potential of leveraging the capabilities of ML with glSNe systems to obtain a pipeline capable of fast and automated $H_0$ measurements.