Fast N-body PM simulations with a small number of time steps such as FastPM or COLA have been remarkably successful in modeling the galaxy statistics, but their lack of small scale force resolution and long time steps cannot give accurate halo matter profiles or matter power spectrum. High resolution N-body simulations can improve on this, but lack baryonic effects, which can only be properly included in hydro simulations. Here we present a scheme to calibrate the fast simulations to mimic the precision of the hydrodynamic simulations or high resolution N-body simulations. The scheme is based on a gradient descent of either effective gravitational potential, which mimics the short range force, or of effective enthalpy, which mimics gas hydrodynamics and feedback. The scheme is fast and differentiable, and can be incorporated as a post-processing step into any simulation. It gives very good results for the matter power spectrum for several of the baryonic feedback and dark matter simulations, and also gives improved dark matter halo profiles. The scheme is even able to find the large subhalos, and increase the correlation coefficient between the fast simulations and the high resolution N-body or hydro simulations. It can also be used to add baryonic effects to the high resolution N-body simulations. While the method has free parameters that can be calibrated on various simulations, they can also be viewed as astrophysical nuisance parameters describing baryonic effects that can be marginalized over during the data analysis. In this view these parameters can be viewed as an efficient parametrization of baryonic effects.