Accelerating HI density predictions during the Epoch of Reionization using a GPR-based emulator on N-body simulations

Building fast and accurate ways to model the distribution of neutral hydrogen during the Epoch of Reionization (EoR) is essential for interpreting upcoming 21 cm observations. A key component of semi-numerical models of reionization is the collapse fraction field $f_{\text{coll}}(\mathbf{x})$, which represents the fraction of mass within dark matter halos at each location. Using high-dynamic range N-body simulations to obtain this is computationally prohibitive and semi-analytical approaches, while being fast, end up compromising on accuracy. In this work, we bridge the gap by developing a machine learning model that can generate $f_{\text{coll}}$ maps by sampling from the full distribution of $f_{\text{coll}}$ conditioned on the dark matter density contrast $\delta$. The conditional distribution functions and the input density field to the model are taken from low-dynamic range N-body simulations that are more efficient to run. We evaluate the performance of our ML model by comparing its predictions to a high-dynamic range N-body simulation. Using these $f_{\text{coll}}$ maps, we compute the HI and HII maps through a semi-numerical code for reionization. We are able to recover the large-scale HI density field power spectra $(k \lesssim 1\ h\,{\rm Mpc}^{-1})$ at the $\lesssim10\%$ level, while the HII density field is reproduced with errors well below 10% across all scales. Compared to existing semi-analytical prescriptions, our approach offers significantly improved accuracy in generating the collapse fraction field, providing a robust and efficient alternative for modeling reionization.