Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently such predictions can only be obtained from costly, precision numerical simulations. The "Coyote Universe'' simulation suite comprises nearly 1,000 N-body simulations at different force and mass resolutions, spanning 38 wCDM cosmologies. This large simulation suite enabled construct of a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k~1 h/Mpc. This is the first cosmic emulator for the dark matter power spectrum.

The concentration-mass relation for dark matter-dominated halos is one of the essential results expected from a theory of structure formation. C-m Emu is a simple numerical code for the c-M relation as a function of cosmological parameters for wCDM models generates the best-fit power-law model for each redshift separately and then interpolate between the redshifts. This produces a more accurate answer at each redshift at the minimal cost of running a fast code for every c -M prediction instead of using one fitting formula. The emulator is constructed from 37 individual models, with three nested N-body gravity-only simulations carried out for each model. The mass range covered by the emulator is 2 x 10^{12} M_sun < M <10^{15} M_sun with a corresponding redshift range of z=0 -1. Over this range of mass and redshift, as well as the variation of cosmological parameters studied, the mean halo concentration varies from c ~ 2 to c ~ 8. The distribution of the concentration at fixed mass is Gaussian with a standard deviation of one-third of the mean value, almost independent of cosmology, mass, and redshift over the ranges probed by the simulations.

Modern cosmological surveys are delivering datasets characterized by unprecedented quality and statistical completeness. In order to maximally extract cosmological information from these observations, matching theoretical predictions are needed. In the nonlinear regime of structure formation, cosmological simulations are the primary means of obtaining the required information but the computational cost of sufficiently resolved large-volume simulations makes it prohibitive to run very large ensembles. Nevertheless, precision emulators built on a tractable number of high-quality simulations can be used to build very fast prediction schemes to enable a variety of cosmological inference studies. The "Mira-Titan Universe" simulation suite covers the standard six cosmological parameters and, in addition, includes massive neutrinos and a dynamical dark energy equation of state. It is based on 111 cosmological simulations, each covering a (2.1Gpc)^3 volume and evolving 3200^3 particles, and augments these higher-resolution simulations with an additional set of 1776 lower-resolution simulations and TimeRG perturbation theory results to cover scales straddling the linear to mildly nonlinear regimes. The emulator built on this suite, the CosmicEmu, provides predictions at the two to three percent level of accuracy over a wide range of cosmological parameters. Presented in: https://arxiv.org/abs/2207.12345.

Ostrich emulates surrogate models for complex and expensive functions using Principal Component Analysis (PCA) to decompose a signal, then interpolate the PCA weights over the parameters θ using a Gaussian Process interpolator. The code is trained on samples from the expensive functions, recreating and interpolating between those training samples with reduced computational cost, and recalculating for each use.