From ANN to BNN: Inferring Reionization Parameters using Uncertainty-aware Emulators of 21-cm Summaries

TL;DR

This work tackles the challenge of inferring Epoch of Reionization (EoR) parameters from non-Gaussian 21-cm signals by leveraging uncertainty-aware emulators. The authors develop Bayesian neural networks (BNNs) to emulate the power spectrum and bispectrum of the 21-cm signal, enabling predictive posteriors that propagate emulator uncertainty into Bayesian parameter inference. Compared with traditional artificial neural networks (ANNs), the BNNs provide tighter, more robust parameter constraints, with particular advantage when using the bispectrum as a summary statistic, which contains richer information about non-Gaussianity. Using mock SKA-LOW observations (1000 hours) at $z=7$ and a semi-numerical excursion-set simulation across 7200 parameter combinations, the study demonstrates that bispectrum-based inference with BNN emulators yields superior constraints and remains robust when training data are scarce. The results highlight the value of uncertainty quantification in forward-model emulators for astrophysical parameter estimation and point to future enhancements, including lightcone modeling, residual foregrounds, and simulation-based inference (SBI) approaches.

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 task. The 21-cm signal from EoR is expected to be highly non-Gaussian; 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 simulations many times, which is computationally very expensive. To overcome this challenge, many artificial neural network (ANN) based emulators have been introduced, which produce the 21-cm summaries in a fraction of the time. However, ANN emulators have a drawback: they can only produce point-value predictions; thus, they fail to capture the uncertainty associated with their 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 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 can 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. We 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.

Figures (8)

• Figure 1: The left panel shows the allowed region (green shade) for $k_2$ spanning the triangles of all unique shapes for a fixed $k_1$. The right panel shows how the different unique shapes (denoted by $\cos \;\chi$) of the triangles are distributed over the $n - \cos \;\mathrm{\theta}$ plane.
• Figure 2: Plot shows the performance of ANN and BNN power spectrum emulators trained on different dataset sizes. The top plot shows the results for the complete dataset, and the bottom plots show the results for $1000$ (left) and $500$ (right) datasets. Here, red and blue lines correspond to the power spectrum prediction of the ANN and BNN emulators, respectively. The blue shaded region is the $3\sigma$ uncertainty associated with the mean prediction by BNN. The true power spectrum is shown with the black line. The bottom panel of each plot shows the percentage errors of the ANN prediction in red and the BNN mean prediction in blue.
• Figure 3: Bispectrum prediction by ANN emulators. The top left panel shows the emulated bispectrum, and the top right panel shows the simulated bispectrum for the same set of EoR parameters. The relative fractional error between the simulated and emulated bispectrum is shown in the lower panel. The islands of the high relative fractional errors mostly correspond to the errors in the sign prediction.
• Figure 4: Bispectrum prediction by BNN emulators. The top left panel shows the mean values of the emulated bispectrum, and the top right panel shows the simulated bispectrum for the same set of EoR parameters. The relative fractional error between the simulated and emulated bispectrum is shown in the lower panel. We can see that the island of high relative errors is overall decreased compared to the ANN prediction.
• Figure 5: Line plots for the two triangle configurations of the bispectrum. The left column shows emulator predictions for equilateral triangle configurations, and the right column shows predictions for squeezed-limit triangle configurations. The red line shows the bispectrum prediction by the ANN, and the blue line shows the prediction by the BNN, with the blue shaded region representing the $3\sigma$ error on the BNN prediction. Both predictions are compared with the simulated bispectrum presented with the black line. The rows represent the size of training datasets used to train the corresponding emulators.