Uncertainty-aware Neural Networks for Fuzzy Dark Matter Model Selection from <i>x</i> _{H <scp>I</scp>} Measurements

Abstract The nature of dark matter remains a central question in cosmology, with fuzzy dark matter (FDM) models offering a compelling alternative to the cold dark matter paradigm. We explore FDM scenarios by performing 21 cm simulations across a parameter space with f FDM ∈ [0.02, 0.10] and m FDM ∈ [10 −24 , 10 −21 ] eV, obtaining global neutral hydrogen fractions ( x H I ) for each model. Observational x H I data and associated uncertainties from the James Webb Space Telescope are incorporated by estimating full probability density functions (pdfs) for both x H I and redshift z using Bayesian inference with the No-U-Turn Sampler, yielding non-Gaussian multivariate uncertainty distributions. A hybrid machine learning framework is then trained on these observational pdfs to learn both central values and correlated uncertainties in x H I and z , iteratively refining its parameters in each training epoch through direct incorporation of the multivariate pdfs derived from observational constraints. We then compare the simulation outputs to the machine-learned observational trends to identify the most consistent models. Our results indicate that FDM models with m FDM ≃ 10 −22 eV and f FDM ≃ 0.04 best match the current data, while lighter masses are strongly constrained. By integrating simulations and machine learning in an uncertainty-aware framework, this work explores the physics of the early Universe and guides future studies of 21 cm cosmology and reionization.