CARPool: fast, accurate computation of large-scale structure statistics
  by pairing costly and cheap cosmological simulations
  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 (COLA). We find
$\sim 100$-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 realises 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 $60\%$ 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 $\sim 10$, 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.
