AI-assisted super-resolution cosmological simulations IV: An emulator for deterministic realizations

Super-resolution (SR) models in cosmological simulations use deep learning (DL) to rapidly enhance low-resolution (LR) runs with statistically correct fine details. These models preserves large-scale structures by conditioning on an LR version of the simulation. On smaller scales, the generative process is inherently stochastic, producing multiple possible SR realizations with distinct small-scale structures. Validation of reconstructed SR runs from LR simulations requires ensuring that specific statistics of interest are accurately reproduced by comparing SR outputs with target high resolution (HR) runs. In this study, we develop an emulator designed to reproduce the small-scale structures of target HR simulation with high fidelity. By processing an SR realization alongside the high-resolution initial condition (HRIC), we transform the SR output to emulate the result of a full simulation with that HRIC. By comparing various metrics, from visualization to individual halo measurements, we demonstrate that the emulated SR runs closely align with the target HR simulation, even at length scales an order of magnitude smaller than the corresponding LR run. These results show the potential of this method for efficiently generating accurate simulations and mock observations for large galaxy surveys.