Inferring Cosmological Parameters on SDSS via Domain-Generalized Neural Networks and Lightcone Simulations

We present a proof-of-concept simulation-based inference on $\Omega_{\rm m}$ and $\sigma_{8}$ from the SDSS BOSS LOWZ NGC catalog using neural networks and domain generalization techniques without the need of summary statistics. Using rapid lightcone simulations, ${\rm L{\scriptsize -PICOLA}}$, mock galaxy catalogs are produced that fully incorporate the observational effects. The collection of galaxies is fed as input to a point cloud-based network, ${\texttt{Minkowski-PointNet}}$. We also add relatively more accurate ${\rm G{\scriptsize ADGET}}$ mocks to obtain robust and generalizable neural networks. By explicitly learning the representations which reduces the discrepancies between the two different datasets via the semantic alignment loss term, we show that the latent space configuration aligns into a single plane in which the two cosmological parameters form clear axes. Consequently, during inference, the SDSS BOSS LOWZ NGC catalog maps onto the plane, demonstrating effective generalization and improving prediction accuracy compared to non-generalized models. Results from the ensemble of 25 independently trained machines find $\Omega_{\rm m}=0.339 \pm 0.056$ and $\sigma_{8}=0.801 \pm 0.061$, inferred only from the distribution of galaxies in the lightcone slices without relying on any indirect summary statistics. A single machine that best adapts to the ${\rm G{\scriptsize ADGET}}$ mocks yields a tighter prediction of $\Omega_{\rm m}=0.282 \pm 0.014$ and $\sigma_{8}=0.786 \pm 0.036$. We emphasize that adaptation across multiple domains can enhance the robustness of the neural networks in observational data.