Dark Energy Survey Year 3 Results: Simulation-based Cosmological Inference with Wavelet Harmonics, Scattering Transforms, and Moments of Weak Lensing Mass Maps. Validation on Simulations

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end -to -end simulationbased analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). We implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven nu wCDM cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for S8, omega m, and the figure-of-merit FoMS8;omega m, respectively. We further find that non-Gaussian statistics improve constraints on w and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.