In this work, we perform a simulation-based forecasting analysis to compare the cosmological constraining power of higher-order summary statistics of the large-scale structure (LSS)—the Minkowski functionals (MFs) and a class weighted morphological measure known as the conditional moments of derivatives (CMD)—with that of the redshift-space halo power spectrum multipoles (PS), with a particular focus on their sensitivity to nonlinear and anisotropic features in redshift space. Our analysis relies on halo catalogs from the big Sobol sequence (BSQ) simulations at redshift $z=0.5$, employing a likelihood-free inference framework implemented via neural posterior estimation. At the fiducial Quijote cosmology $({\mathrm{\Omega }}_{\mathrm{m}}=0.3175,{\sigma }_8=0.834)$ and for a Gaussian smoothing scale of $R=15h^{-1}\mathrm{Mpc}$, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by $27{\%}_{-5\%}^{+9\%}$ for ${\sigma }_8$ and $26{\%}_{-5\%}^{+7\%}$ for ${\mathrm{\Omega }}_{\mathrm{m}}$ relative to MFs alone, highlighting the complementary anisotropy-sensitive information captured by the CMD in contrast to the scalar morphological content encapsulated by the MFs. We compare the combined statistic $\mathrm{MFs}+\mathrm{CMD}$ with the PS at matched effective scales ($k_{\max }\simeq 0.16h{\mathrm{Mpc}}^{-1}$) under three halo-selection conditions: (i) all halos, (ii) fixed number density, and (iii) mass-selected ($M>3\times {10}^{13}{h}^{-1}{M}_{\odot }$). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by $45{\%}_{-9\%}^{+20\%}$ for ${\sigma }_8$ and $43{\%}_{-7\%}^{+10\%}$ for ${\mathrm{\Omega }}_{\mathrm{m}}$. We also extend the simulation-based forecast analysis across a continuous range of cosmological parameters and multiple smoothing scales for (weighted) morphological measures. While the absolute uncertainties depend on parameter values and smoothing scale, the relative constraining power of the summary statistics remains nearly constant.

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• Cosmological parameters
• Large scale structure of the Universe
• Machine learning