Inferring the density, spin-temperature and neutral-fraction fields of HI from its 21-cm brightness temperature field using machine learning

The 21-cm brightness-temperature field of neutral hydrogen during the Epoch of Reionization and Cosmic Dawn is a rich source of cosmological and astrophysical information, primarily due to its significant non-Gaussian features. However, the complex, nonlinear nature of the underlying physical processes makes analytical modelling of this signal challenging. Consequently, studies often resort to semi-numerical simulations. Traditional analysis methods, which rely on a limited set of summary statistics, may not adequately capture the non-Gaussian content of the data, as the most informative statistics are not predetermined. This paper explores the application of machine learning (ML) to surpass the limitations of summary statistics by leveraging the inherent non-Gaussian characteristics of the 21-cm signal. We demonstrate that a well-trained neural network can independently reconstruct the hydrogen density, spin-temperature, and neutral-fraction fields with cross-coherence values exceeding 0.95 for $k$-modes below $0.5$ Mpc h$^{-1}$, based on a representative simulation at a redshift of $z \approx 15$. To achieve this, the neural network utilises the non-Gaussian information in brightness temperature images over many scales. We discuss how these reconstructed fields, which vary in their sensitivity to model parameters, can be employed for parameter inference, offering more direct insights into underlying cosmological and astrophysical processes only using limited summary statistics of the brightness temperature field, such as its power spectrum.