Ten-parameter simulation suite for cosmological emulation beyond $\Lambda$CDM

We present Goku, a suite of cosmological $N$-body simulations, and the corresponding 10-dimensional emulator, GokuEmu, for the nonlinear matter power spectrum. The simulations span the base parameters of $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmology and its extensions, including dynamical dark energy ($w_0$, $w_a$), the sum of the neutrino masses ($\sum m_\nu$), the effective number of neutrinos ($N_\text{eff}$), and the running of the scalar spectral index ($\alpha_\text{s}$), enabling tests of new physics with data from upcoming surveys like the Roman Space Telescope, Euclid, and LSST. Designed within the MF-Box framework, which integrates multi-scale and multi-fidelity simulations, the suite includes high-fidelity simulations evolving $3000^3$ particles in $1\,(\text{Gpc}/h)^3$ volumes and low-fidelity simulations with $750^3$ particles across varying box sizes. This approach achieves percent-level accuracy in high-likelihood regions and 5% accuracy across broader parameter ranges, while reducing computational costs by 94% compared to single-fidelity methods. The simulations adopt an accurate treatment of massive neutrinos, enhancing predictions of the matter power spectrum on nonlinear scales. Key innovations include an adaptive sampling strategy and the use of beam search to optimize generalization accuracy. The emulator is valid for redshifts $z \leq 3$ and scales $0.01 \lesssim k / (h \, \text{Mpc}^{-1}) \lesssim 10$. Beyond the matter power spectrum, the simulations also support analyses of other statistical measures, such as the halo mass function. The emulator and its training data are publicly available at https://github.com/astro-YYH/GokuEmu, providing a valuable resource for cosmological parameter inference and model testing.