Surveys aiming at supernovae include initiatives to find them. Spotting them quickly so as to gather data early in their life is a particular challenge. The Rubin Observatory (LSST) will likely handle much of this, at least for those not at cosmological distances. Some efforts to find them use data from near-Earth object and other solar system surveys, currently notably Pan-STARRS, as well as other general surveys for transients such as the Zwicky Transient Facility, and other surveys that cover a lot of the celestial sphere quickly, such as Gaia.
Surveys specifically of Type Ia supernovae (Type Ia supernova surveys) have been of interest in cosmology, as standard candles to help determine the Hubble constant. They where instrumental in recognizing the acceleration motivating the concept of dark energy.
Some surveys dedicated to or including supernovae: