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To exploit the power of next-generation large-scale structure surveys,ensembles of numerical simulations are necessary to give accurate theoreticalpredictions of the statistics of observables. High-fidelity simulations come ata towering computational cost. Therefore, approximate but fast simulations,surrogates, are widely used to gain speed at the price of introducing modelerror. We propose a general method that exploits the correlation betweensimulations and surrogates to compute fast, reduced-variance statistics oflarge-scale structure observables without model error at the cost of only a fewsimulations. We call this approach Convergence Acceleration by Regression andPooling (CARPool). In numerical experiments with intentionally minimal tuning,we apply CARPool to a handful of GADGET-III $N$-body simulations paired withsurrogates 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 nearlylinear regime CARPool attains far larger sample variance reductions. Bycomparing to the 15,000 simulations from the Quijote suite, we verify that theCARPool estimates are unbiased, as guaranteed by construction, even though thesurrogate misses the simulation truth by up to $60\%$ at high $k$. Furthermore,even with a fully configuration-space statistic like the non-linear matterdensity probability density function, CARPool achieves unbiased variancereduction factors of up to $\sim 10$, without any further tuning. Conversely,CARPool can be used to remove model error from ensembles of fast surrogates bycombining them with a few high-accuracy simulations.

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