Generative models of astrophysical fields with scattering transforms on the sphere

Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build generative models of complex non-linear fields from a limited amount of data and have been used as the basis of new statistical component separation algorithms. In the context of upcoming cosmological surveys, such as LiteBIRD for the cosmic microwave background polarisation or the Vera C. Rubin Observatory and the Euclid space telescope for study of the large-scale structures of the Universe, extending these tools to spherical data is necessary. In this work, we developed scattering transforms on the sphere and focused on the construction of maximum-entropy generative models of several astrophysical fields. We constructed, from a single target field, generative models of homogeneous astrophysical and cosmological fields, whose samples were quantitatively compared to the target fields using common statistics (power spectrum, pixel probability density function, and Minkowski functionals). Our sampled fields agree well with the target fields, both statistically and visually. We conclude, therefore, that these generative models open up a wide range of new applications for future astrophysical and cosmological studies, particularly those for which very little simulated data is available.