Reconstruction of Reionization Histories from 21 cm Power-Spectrum Evolution with Artificial Neural Networks

We investigate whether the redshift evolution of the fixed-$k$ dimensionless 21 cm power spectrum, $\Delta^2_{21}(k, z)$, contains sufficient information to reconstruct reionization histories $x_{\mathrm{HI}}(z)$ with artificial neural networks. Using semi-numerical realizations generated within a restricted three-parameter 21cmFAST model family, we train a compact feed-forward network to learn the inverse mapping from power-spectrum trajectories to the neutral-fraction history over $6 \le z \le 15$. For $k = 0.1$, $0.5$, and $1.0\ h\ \mathrm{Mpc}^{-1}$, representative tests on an independent test set show that the midpoint redshift $z_{50}$ is recovered more accurately than the duration $\Delta z = z_{75} - z_{25}$: $z_{50}$ is reconstructed with MAE = 0.0046 and RMSE = 0.0100, whereas $\Delta z$ yields MAE = 0.0302 and RMSE = 0.0378. This result indicates that fixed-$k$ power-spectrum evolution carries stronger information about the timing of reionization than about the detailed width of the transition within the adopted prior. We further test an idealized foreground-free SKA1-Low-like thermal-plus-sample-variance noise model and find that the reconstruction remains stable in the favorable signal-to-noise regime considered here. These results demonstrate that neural networks can serve as prior-dependent inverse mapping for reconstructing reionization histories from 21 cm power-spectrum evolution.