A series techniques have been devised to reconstruct the current and initial density and velocity fields from galaxy redshift surveys. These approaches have been applied to the SDSS DR7, covering the redshift range $0.01 \lesssim z \lesssim 0.12$, enabling the reconstruction of the initial conditions of the local universe. Subsequently, forward N-body and hydrodynamic simulations have been conducted using these reconstructed initial conditions, leading to the accurate reproduction of the statistical characteristics of both the cosmic web and the halo population. Further investigations into the galaxy model and cosmic variance are currently being pursued, leveraging the environmental information made available by the reconstruction.

Constrained N-body and hydrodynamic simulations have been conducted using the reconstructed initial conditions that cover the SDSS survey volume. The simulations encompass a variety of scales and regions, including:

• a N-body simulation featuring a box with dimensions of $500 {h^{-1}{\rm Mpc}}^3$ and $3072^3$ particles, which covers the entire reconstructed volume of the SDSS NGC ($0.01 \lesssim z \lesssim 0.12$);
• zoom-in hydrodynamic simulations in three distinct regions: the Coma cluster, the SDSS great wall, and a large low-density region at $z\sim 0.05$;
• empirical models for galaxies based on (sub)halo data for the entire reconstructed volume.