# High mass and halo resolution from fast low resolution simulations

## TL;DR

This paper develops calibration techniques for fast low resolution simulations to accurately reproduce halo and matter statistics, enabling efficient generation of large-scale mock catalogs for future sky surveys.

## Contribution

It introduces a relaxed-FOF halo finder and incorporates the potential gradient descent method to enhance the accuracy of fast simulations, making them comparable to high-resolution N-body simulations.

## Key findings

- Relaxed-FOF improves halo bias and mass function accuracy.
- PGD method enhances matter distribution and weak lensing spectra.
- FastPM achieves high accuracy with significantly fewer time steps.

## Abstract

Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. In this work we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition accuracy and develop a halo finder "relaxed-FOF", where we allow different linking length for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum in real space and in redshift space, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scale. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.