scholarly journals CARPool: fast, accurate computation of large-scale structure statistics by pairing costly and cheap cosmological simulations

2021 ◽  
Vol 503 (2) ◽  
pp. 1897-1914
Author(s):  
Nicolas Chartier ◽  
Benjamin Wandelt ◽  
Yashar Akrami ◽  
Francisco Villaescusa-Navarro

ABSTRACT To exploit the power of next-generation large-scale structure surveys, ensembles of numerical simulations are necessary to give accurate theoretical predictions of the statistics of observables. High-fidelity simulations come at a towering computational cost. Therefore, approximate but fast simulations, surrogates, are widely used to gain speed at the price of introducing model error. We propose a general method that exploits the correlation between simulations and surrogates to compute fast, reduced-variance statistics of large-scale structure observables without model error at the cost of only a few simulations. We call this approach Convergence Acceleration by Regression and Pooling (CARPool). In numerical experiments with intentionally minimal tuning, we apply CARPool to a handful of gadget-iii  N-body simulations paired with surrogates computed using COmoving Lagrangian Acceleration. We find ∼100-fold variance reduction even in the non-linear regime, up to $k_\mathrm{max} \approx 1.2\, h {\rm Mpc^{-1}}$ for the matter power spectrum. CARPool realizes similar improvements for the matter bispectrum. In the nearly linear regime CARPool attains far larger sample variance reductions. By comparing to the 15 000 simulations from the Quijote suite, we verify that the CARPool estimates are unbiased, as guaranteed by construction, even though the surrogate misses the simulation truth by up to $60{{\ \rm per\ cent}}$ at high k. Furthermore, even with a fully configuration-space statistic like the non-linear matter density probability density function, CARPool achieves unbiased variance reduction factors of up to ∼10, without any further tuning. Conversely, CARPool can be used to remove model error from ensembles of fast surrogates by combining them with a few high-accuracy simulations.

2014 ◽  
Vol 11 (S308) ◽  
pp. 121-124
Author(s):  
Hélène Dupuy

AbstractThere is now no doubt that neutrinos are massive particles fully involved in the non-linear growth of the large-scale structure of the universe. A problem is that they are particularly difficult to include in cosmological models because the equations describing their behavior in the non-linear regime are cumbersome and difficult to handle. In this manuscript I present a new method allowing to deal with massive neutrinos in a very simple way, based on basic conservation laws. This method is still valid in the non-linear regime. The key idea is to describe neutrinos as a collection of single-flow fluids instead of seeing them as a single hot multi-flow fluid. In this framework, the time evolution of neutrinos is encoded in fluid equations describing macroscopic fields, just as what is done for cold dark matter. Although valid up to shell-crossing only, this approach is a further step towards a fully non-linear treatment of the dynamical evolution of neutrinos in the framework of large-scale structure growth.


2020 ◽  
Vol 499 (2) ◽  
pp. 1769-1787
Author(s):  
Anaëlle Halle ◽  
Takahiro Nishimichi ◽  
Atsushi Taruya ◽  
Stéphane Colombi ◽  
Francis Bernardeau

ABSTRACT The power spectrum response function of the large-scale structure of the Universe describes how the evolved power spectrum is modified by a small change in initial power through non-linear mode coupling of gravitational evolution. It was previously found that the response function for the coupling from small to large scales is strongly suppressed in amplitude, especially at late times, compared to predictions from perturbation theory (PT) based on the single-stream approximation. One obvious explanation for this is that PT fails to describe the dynamics beyond shell crossing. We test this idea by comparing measurements in N-body simulations to prescriptions based on PT but augmented with adaptive smoothing to account for the formation of non-linear structures of various sizes in the multistream regime. We first start with one-dimensional (1D) cosmology, where the Zel’dovich approximation provides the exact solution in the single-stream regime. Similarly to the three-dimensional (3D) case, the response function of the large-scale modes exhibits a strong suppression in amplitude at small scales that cannot be explained by the Zel’dovich solution alone. However, by performing adaptive smoothing of initial conditions to identify haloes of different sizes and solving approximately post-collapse dynamics in the three-stream regime, agreement between theory and simulations drastically improves. We extend our analyses to the 3D case using the pinocchio algorithm, in which similar adaptive smoothing is implemented on the Lagrangian PT fields to identify haloes and is combined with a spherical halo prescription to account for post-collapse dynamics. Again, a suppression is found in the coupling between small- and large-scale modes and the agreement with simulations is improved.


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