Primordial non-Gaussianity -- Fast simulations and persistent summary statistics

We investigate the sensitivity of topological and traditional summary statistics to primordial non-Gaussianity (PNG) using two suites of simulations. First, we introduce a new simulation suite for PNG, PNG-pmwd, comprising more than $20{,}000$ halo catalogs that vary individually local and equilateral shapes, together with variations in $\Omega_m$ and $\sigma_8$. Second, we carry out a systematic comparison of topological descriptors, as well as powerspectrum and bispectrum measurements, evaluating their constraining power on both local and equilateral $f_{\rm NL}$ and how this sensitivity varies with halo mass. This dataset enables likelihood-free neural regression of $f_{\rm NL}$ across multiple halo mass bins for a wide range of summary statistics. Third, we assess the transferability of these learned mappings by testing whether models trained on fast pmwd simulations can robustly infer on simulations from the QuijotePNG suite. We find that a combination of simple descriptive statistics of the topological features (PD-statistics) leads to the best performance to constrain equilateral PNG. We observe that the constraining power of these summaries comes from large-mass halos, with small-mass halos adding noise and degrading performance. Similarly, we find that the transferability of the learned mappings, for both topological and powerspectrum plus bispectrum, degrades if small scales or small-mass halos are included.