Implicit inference of the reionization history with higher-order statistics of the 21-cm signal
SKACH Winter Days, CSCS, Lugano, January 2026
Nicolas Cerardi
On behalf of the SEarCH team: Sambit Giri, Michele Bianco, Davide Piras, Emmanuel de Salis, Massimo de Santis, Merve Selcuk-Simsek, Philipp Denzel, Kelley Hess, Carmen Toribio, Franz Kirsten & Hatem Ghorbel
- Participated to the SKA Data Challenge 3b: Inference
- Goal: infer the neutral fraction $ \bar{x}_{\rm HI} $ in SKA-Low mocks at three different $ z $ to constrain the Epoch of Reionisation
Our strategy
-
Created a large dataset of ~16000 SKA-Low mocks
- Included instrumental noise but no foregrounds
-
Trained 2 independent DL approaches
- Regression task on $ \bar{x}_{\rm HI} $ with deep CNNs
[De Salis+25]
- Bayesian inference with Simulation-based Inference (SBI)
- Regression task on $ \bar{x}_{\rm HI} $ with deep CNNs
"I have a complex and noisy model which doesn't provide an explicit likelihood"
$ \Rightarrow $ learn the posterior directly from simulations !
$ \Rightarrow $ learn the posterior directly from simulations !
- Obtained great results on the PS2 data 🎉
- But not ranked on the PS1 data
Goals of today's talk
- Go beyond the data challenge with higher-order statistics
- Give details on our SBI strategy
- Provide statistically robust results
- Rejecting extreme reionisation cases
- Dataset expanded x2 with more noise realisation applied on the mocks
- Test the noise-level dependence: 100h and 1000h SKA-Low noise considered
- More statistics computed from the mocks
We compute several kinds of statistics $ t $ from the 21cm cubes
2pt statistics
1D Power Spectrum
2D Power Spectrum
Higher-order statistics
Bispectrum (equilateral & squeezed)
Betti numbers (topological invariant)
+ combinations of these metrics
- $ \bar{x}_{\rm HI} $ is an output of the simulation: we do not directly sample it
- Prior on $ \bar{x}_{\rm HI} $ is implicit and non-trivial
- Direct neural posterior estimation is the way to go !
\[\begin{aligned}
p(\bar{x}_{\rm HI} | t) & \propto p(\bar{x}_{\rm HI}) p(t | \bar{x}_{\rm HI}) \\ & \propto q_\phi (\bar{x}_{\rm HI} | t)
\end{aligned} \]
- We are model-dependent on both the prior and the likelihood
We apply Variational Mutual Information Maximization (VMIM, Jeffrey+20) to learn $ p(\bar{x}_{\rm HI} | t) $ by:
- Compressing the stacked statistics $ [t_1, t_2, t_3] $ into a 3D vector $ y $
- Maximizing the mutual information between $ y $ and $ \bar{x}_{HI} $
SBI studies should always provide robust statistical validation of the learnt posteriors
- For each case we train 20+ models to check for the stability of our approach
- We systematically perform coverage tests and select the best model for each case
Test of Accuracy with Random Points (TARP) runs on the validation set for different cases
- $ \sigma(\bar{x}_{\rm HI}) $ decreases by ~40% from 100h to 1000h (but very statistic dependent)
- PS2D + higher order stats: $ \sigma(\bar{x}_{\rm HI}) $ decreases by ~60% at 100h and ~40% at 1000h
- Betti numbers are more informative towards the end of EoR
- Power spectrum is more constraining in the early EoR
- Bispectrum mildly contributes to early EoR constraints
Conclusions
- Based on our work for SDC3b, we investigated the reionisation history through several summary statistics
- We employed 2-pt statistics (1D and 2D power spectra) with higher order statistics (bispectrum and Betti numpers)
- We applied a SBI framework to infer parameters from these statistics
- Betti numbers (alone and combined with others) are particularly promising
- We also identify different regimes of relevance for each statistic
[Cerardi et al., submitted to MNRAS, 2025]
