Simulation budgeting for hybrid effective field theories

In this work, we forecast the number of, and requirements on, N-body simulations needed to train hybrid effective field theory (HEFT) emulators for a range of use cases, using a hybrid of HMcode and perturbation theory as a surrogate model. Our accuracy goals, determined with careful consideration of statistical and systematic uncertainties, are $1\%$ accurate in the high-likelihood range of cosmological parameters, and $2\%$ accurate over a broader parameter space volume for $k<1 h Mpc^{-1}$ and $z<3$. Focusing in part on the 8-parameter $w_0w_a$CDM+$m_\nu$ cosmological model, we find that $<225$ simulations are required to meet our error goals over our wide parameter space, including models with rapidly evolving dark energy, given our simulation and emulator recommendations. For a more restricted parameter space volume, as few as 80 simulations are sufficient. We additionally present simulation forecasts for example use cases, and make the code used in our analyses publicly available. These results offer practical guidance for efficient emulator design and simulation budgeting in future cosmological analyses.