Representing Core-collapse Supernova Light Curves Analytically with Symbolic Regression

In anticipation of new astrophysical surveys such as the upcoming Legacy Survey of Space and Time conducted by the Vera C. Rubin Observatory, machine learning techniques are increasingly used to rapidly classify transient events in the night sky. Most often, deep-learning based methods rely on unphysical and uninterpretable representations of astrophysical data. In this work, we use symbolic regression to derive an analytic expression for the luminosity of the most common core-collapse supernova (the explosive death of a massive star) as a function of time and physical parameters--an analytical expression for these events has eluded the literature for a century. This expression is trained from a set of simulated bolometric light curves (measured luminosity as a function of time) generated from six input physical parameters. We find that a single analytic expression can adequately reproduce ~70% of light curves in our dataset; we additionally present a small set of analytical expressions to reproduce the full set of light curves. By deriving an analytic relation between physical parameters and light curve fluxes, we create (for the first time) an interpretable parametric model and circumvent the computationally expensive integrations used to simulate the original dataset. This work demonstrates promising preliminary results for future efforts to make machine learning techniques in astronomy more transparent and interpretable.