In this paper, we turn to the learning the Universe implicit likelihood inference pipeline to perform a multiround implicit likelihood inference of the neutrino mass hierarchy from cosmological data, including $TT$, $TE$, and $EE$ power spectra of Planck 2018 and distance ratios of DESI DR2. More precisely, we first embed the CMB power spectra simulator class into the learning the Universe implicit likelihood inference pipeline. And then, opting for sequential neural likelihood estimation, we sequentially train neural networks using six rounds of 10000 simulations to target a “black box” likelihood of our forward model with one additional neutrino mass hierarchy parameter $\tilde{\mathrm{\Delta }}$ and six base cosmological parameters. We find $\tilde{\mathrm{\Delta }}=0.12_{-0.23}^{+0.21}$ (68% confidence level).

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• Baryon acoustic oscillations
• Cosmic microwave background
• Cosmological parameters
• Cosmology
• Astrophysical & cosmological simulations