  The hyperfine structure absorption lines of neutral hydrogen in spectra of
high-redshift radio sources, known collectively as the 21-cm forest, have been
demonstrated as a sensitive probe to the small-scale structures governed by the
dark matter (DM) properties, as well as the thermal history of the
intergalactic medium regulated by the first galaxies during the epoch of
reionization. By statistically analyzing these spectral features, the
one-dimensional (1D) power spectrum of the 21-cm forest can effectively break
the parameter degeneracies and constrain the properties of both DM and the
first galaxies. However, conventional parameter inference methods face
challenges due to computationally expensive simulations for 21-cm forest and
the non-Gaussian signal characteristics. To address these issues, we introduce
generative normalizing flows for data augmentation and inference normalizing
flows for parameters estimation. This approach efficiently estimates parameters
from minimally simulated datasets with non-Gaussian signals. Using simulated
data from the upcoming Square Kilometre Array (SKA), we demonstrate the ability
of the deep learning-driven likelihood-free approach to generate accurate
posterior distributions, providing a robust and efficient tool for probing DM
and the cosmic heating history using the 1D power spectrum of 21-cm forest in
the era of SKA. This methodology is adaptable for scientific analyses with
other unevenly distributed data.
