In this paper, we turn to the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline to perform a multi-round ILI of the neutrino mass hierarchy from cosmological data, including $TT$, $TE$, $EE$ power spectra of Planck 2018 and distance ratios of DESI DR2. More precisely, we first embed the CMB power spectra simulator $\mathtt{ CLASS}$ into the LtU-ILI pipeline. And then, opting for Sequential Neural Likelihood Estimation (SNLE), we sequentially train neural networks using $2$ rounds of $5000$ simulations to target a ``black box'' likelihood of our forward model with one additional neutrino mass hierarchy parameter $\tilde{ \Delta}$ and six base cosmological parameters. We find that $\tilde{ \Delta}=0.12216^{ +0.26193}_{ -0.29243}~(68\%{ \rm CL})$ which slightly prefers $\tilde{ \Delta}>0$, hence the normal hierarchy.
Categories: astro-ph.CO