ELUCID is a method to reconstruct the initial linear density field from an input nonlinear density field,
employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics.
My talk will describe its application and the constrained N-body and gas simulations in the SDSS volume. I will
show how to use the reconstruction to understand galaxies and gas in the cosmic web, as well as the underlying