Generative models of 21 cm Epoch of Reionisation lightcones with 3D scattering transforms

The 21 cm signal from the Epoch of Reionisation (EoR) is observed as a 3D dataset known as a lightcone, consisting of two spatial sky plane axes and a redshift (frequency) axis. Owing to its strongly non-Gaussian nature, fully characterising this signal requires summary statistics that go beyond two-point power spectra statistics. Recent developments in astrophysics, particularly in the context of the Galactic interstellar medium, demonstrate the efficacy of scattering transforms–novel summary statistics–to characterise fields with highly non-Gaussian properties. In particular, these statistics allow us to construct maximum-entropy generative models, even from a single target map, from which we can sample new, almost statistically identical realisations of a given process. Motivated by these advances, we extended the scattering transform formalism from 2D datasets to 3D EoR lightcones. To this end, we introduced a 3D wavelet set from the tensor product of 2D isotropic wavelets in the sky plane domain and 1D wavelets in the redshift domain. To test how well this 3D scattering transform can characterise an EoR lightcone, we constructed a maximum entropy generative model of EoR lightcones, which we quantitatively validated by comparing the new synthesised EoR lightcones with the single target lightcone from which the model is defined. Using independent statistics such as the power spectrum, histograms, and Minkowski functionals, we show that the synthesised lightcones agree very well with the target lightcone, both statistically and visually. The success of these generative models in quickly generating EoR lightcones, which can be extended to a broad range of 3D and heterogeneous 2+1D data, opens up a variety of potential applications, from forward modelling to uncertainty quantification.