The DESI $N$-body Simulation Project -- II. Suppressing sample variance with fast simulations

Abstract

Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise 3D map of our Universe. The survey effective volume reaches ∼ 20 Gpc 3 ℎ −3 . It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with 200 Gpc 3 ℎ −3 (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-𝑁-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variances than the expected DESI statistical variance at the scales we are interested in, e.g., 𝑘 < 0.3 ℎMpc −1 . We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effective volume ∼ 20 times. In summary, our proposed strategy of combining high fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

Validating galaxy clustering models with Fixed & Paired and Matched-ICs simulations: application to Primordial Non-Gaussianities

“…Again, the results are found very similar for the 𝑓 NL = 0 and the 𝑓 NL = 100 cases. The Fixed shows a scale-dependent variance reduction similar to Chuang et al (2019), (Ding et al 2022) or (Maion et al 2022), which we fit here with a smooth step function (Equation 13) that we use for the rest of the paper. When adding the Pairing to the Normal simulations, we actually obtain an increment on the variance at large scales in line with Chuang et al (2019), which goes in opposite direction to the original motivation.…”

“…This is mentioned in several works like Smith & Angulo (2019), however, the correlation coefficient was not explicitly applied to reduce the uncertainty in the analysis. The correlation between Matched-ICs of simulations has been explicitly used in the CARPool method (Chartier et al 2021;Ding et al 2022) but, in that case, between highfidelity mocks and approximate mocks, in order to retrieve unbiased precise clustering statistics from the approximate mocks. Here, we propose a framework to explicitly use the correlation between simulations with Matched-ICs across different cosmologies to reduce the expected variance of the summary statistic and to constrain models to an increased accuracy.…”

Fast and realistic large-scale structure from machine-learning-augmented random field simulations

“…Additionally, we believe that the procedure outlined in this paper could be applied to augment analytical approximations to 𝑁-body simulations (like L-PICOLA, Howlett et al 2015, or FastPM, Feng et al 2016, as well as semi-analytical models of galaxies, which, in the same vein as lognormal random fields, provide a fast approximation to hydrodynamical simulations by modelling complicated baryonic processes (White & Frenk 1991;Kauffmann et al 1993;Cole et al 1994;Somerville & Primack 1999;Lacey 2001). We further plan to explore the possibility to employ the dataset described in this work to reduce the variance in the statistics of large-scale structure observables using a small number of expensive simulations Ding et al 2022), as well as to replace our WGAN-GP model with either a possibly more stable GAN version (Kwon et al 2021), or with a more compact model, like the one proposed in the context of Lagrangian deep learning (LDL, Dai & Seljak 2021), using graph neural networks (GNNs, see e.g. Zhou et al 2018 for a review) or through normalising flows (e.g.…”

Bayesian Control Variates for optimal covariance estimation with pairs of simulations and surrogates

“…The key idea is to combine a small number of costly simulations with a large number of correlated surrogates. Very recently, Ding et al (2022) tested the CARPool principle to estimate the mean of the two-point and three-point clustering statistics of halos, in order to prepare the high-resolution simulations needed for the Dark Energy spectroscopic Instrument (DESI). By pairing AbacusSummit suite (Maksimova et al 2021) simulations with FastPM approxima-tions, they found ≈ 100 times smaller variances with CARPool at scales 𝑘 ≤ 0.3 ℎMpc −1 than with high-resolution simulations alone.…”