Astronomical PSF characterization using grammar evolution and symbolic regression

Abstract

Symbolic regression techniques are promising approaches to learning mathematical models that fit experimental data. One of the most powerful techniques for symbolic regression is Grammatical Evolution (GE). This evolutionary computation technique explores a space of candidate models that are ensured to be syntactically correct expressions built from a set of arbitrary building blocks and operators. In GE the syntax for these expressions is defined by a problem-specific formal grammar. Therefore, GE can produce an explainable solution (e.g. a formula), not a black-box model. The current contribution assesses the viability of GE for PSF characterization, using real datasets from HST/WFPC2. Our experiments show that our method is able to find the most likely candidate mathematical expression for the PSF shape and can also model combinations of shapes taken from a predefined family of functions commonly used in astronomy (Gaussian and Moffat PSFs). These results support the hypothesis that the expressive power of GE can be used to tackle the problem of characterization of complex PSF functions, for example, as a necessary step in the prediction of intra-pixel position of stars.