NoAM for No Action Method is a framework for reconstructing the past orbits of observed tracers of the large scale mass density field. It seeks exact solutions of the equations of motion (EoM), satisfying initial homogeneity and the final observed particle (tracer) positions. The solutions are found iteratively reaching a specified tolerance defined as the RMS of the distance between reconstructed and observed positions. Starting from a guess for the initial conditions, NoAM advances particles using standard N-body techniques for solving the EoM. Alternatively, the EoM can be replaced by any approximation such as Zeldovich and second order perturbation theory (2LPT). NoAM is suitable for billions of particles and can easily handle non-regular volumes, redshift space, and other constraints. We implement NoAM to systematically compare Zeldovich, 2LPT, and N-body dynamics over diverse configurations ranging from idealized high-res periodic simulation box to realistic galaxy mocks. Our findings are (i) Non-linear reconstructions with Zeldovich, 2LPT, and full dynamics perform better than linear theory only for idealized catalogs in real space. For realistic catalogs, linear theory is the optimal choice for reconstructing velocity fields smoothed on scales > 5 Mpc/h. (ii) all non-linear back-in-time reconstructions tested here, produce comparable enhancement of the baryonic oscillation signal in the correlation function.
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