A Machine Learning Approach to Measuring Time Delays in Microlensed Type la Supernovae

Abstract

The discrepancy between early and late-Universe measurements of the Hubble constant, commonly referred to as the Hubble tension, remains one of the most significant open problems in modern cosmology. Strongly-lensed Type Ia supernovae provide a promising and independent probe of the cosmic expansion rate through time-delay cosmography, but their practical application is hindered by microlensing distortions and limited observational cadence. In this work, we present a machine-learning–based method for estimating time delays in microlensed Type Ia supernova light curves. Using realistically simulated lensed supernova datasets, we train and evaluate a Random Forest regression model to recover time delays between unresolved image pairs. We show that data-driven approaches can mitigate microlensing-induced biases relative to traditional cross-correlation methods and recover delays with improved robustness under challenging observational conditions. While this study does not perform a full cosmological inference, the results demonstrate the potential role of machine-learning techniques in future time-delay cosmography pipelines aimed at addressing the Hubble constant tension.