CARPool: fast, accurate computation of largescale structure statistics by pairing costly and cheap cosmological simulations
Abstract
To exploit the power of nextgeneration largescale structure surveys, ensembles of numerical simulations are necessary to give accurate theoretical predictions of the statistics of observables. Highfidelity 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, reducedvariance statistics of largescale 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 GADGETIII Nbody simulations paired with surrogates computed using COmoving Lagrangian Acceleration. We find ∼100fold variance reduction even in the nonlinear 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 configurationspace statistic like the nonlinear 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 highaccuracy simulations.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2021
 DOI:
 10.1093/mnras/stab430
 arXiv:
 arXiv:2009.08970
 Bibcode:
 2021MNRAS.503.1897C
 Keywords:

 methods: statistical;
 cosmology: largescale structure of Universe;
 software: simulations;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 18 pages, 18 figures. v2: Improved and published version