From ANN to BNN: Inferring reionization parameters using uncertainty-aware emulators of 21-cm summaries

Abstract

Inferring astrophysical parameters from radio interferometric observations of the redshifted 21-cm signal from the Epoch of Reionization (EoR) is a challenging, yet crucial. A Bayesian inference pipeline for reionization parameter estimation, forward models the signal statistic, usually the power spectrum, and compares it to the observed statistic. However, the 21-cm signal coming from EoR is expected to be highly non-Gaussian in nature

therefore, we need to use higher-order statistics, e.g., bispectrum. Moreover, the forward modeling of the signal and its statistics for a varying set of model parameters requires rerunning the numerical simulations a large number of times, which is computationally very expensive and time-consuming. To overcome this challenge, many artificial neural network (ANN) based emulators have been introduced, which produce the 21-cm signal summary statistics in a fraction of the time, given input astrophysical parameters. However, ANN emulators have a fundamental drawback: they can only produce point-value predictions

thus, they fail to capture the uncertainty associated with their own predictions. Therefore, when such emulators are used in the Bayesian inference pipeline, they cannot naturally propagate their prediction uncertainties to the estimated model parameters. To address this problem, we have developed Bayesian neural network (BNN) emulators for the 21-cm signal statistics, which provide the posterior distribution of the predicted signal statistics, including their own prediction uncertainty. We use these BNN emulators in our Bayesian inference pipeline to infer the EoR parameters through 21-cm summaries of the mock observation of 21-cm signal with telescopic noise for 1000 hr of SKA-LOW observation. We show that BNN emulators are able to capture the prediction uncertainty for the 21-cm power spectrum and bispectrum, and using these emulators in the inference pipeline provides better and tighter constraints on them. To check the robustness of the emulators, we systematically reduced the training dataset and showed that, for smaller training datasets, BNN outperforms the ANN emulators. We also show that using the bispectrum as a summary statistic gives better constraints on EoR parameters than the power spectrum. © 2025 IOP Publishing Ltd and Sissa Medialab. All rights, including for text and data mining, AI training, and similar technologies, are reserved.