Deriving an Analytical Expression for the Rise of Type Ia Supernovae with Symbolic Regression and High Cadence data

Early excess emission in Type Ia supernovae light curves provides a direct clue to the progenitor systems and explosion mechanism of these standardizable candles. Yet the traditional baseline model, i.e., the empirical ‘power-law’ model developed from low cadence data, is increasingly limited for modern high cadence data due to its restricted time coverage and sensitivity to the chosen fitting window. Here we use symbolic regression to search for compact analytic descriptions of sub-hour-cadence SNe Ia light curves observed by TESS and Kepler, and examine whether events with early excess emission occupy a distinct region of the learned parameter space. Our approach is able to discover functions with inherent invariance and separate different light curve components. We find that a model combining quadratic and sinusoidal terms provides the best description of the observed rise. These preliminary results demonstrate the potential of symbolic regression as an interpretable, data-driven approach for discovering empirical structure in astronomical data.