Uncertainty-Aware Neural Networks for Fuzzy Dark Matter Model Selection from {xHI}{x_HI} Measurements

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 (CDM) paradigm. We explore FDM scenarios by performing 21-cm simulations across a parameter space with {fFDM ∈ [0.02, 0.10]}{f_FDM in [0.02, 0.10]} and {mFDM ∈ [10⁻²⁴, 10⁻²¹]\,eV}{m_FDM in [10^-24, 10^-21] eV}, obtaining global neutral hydrogen fractions ({xHI}{x_HI}) for each model. Observational {xHI}{x_HI} data and associated uncertainties from JWST are incorporated by estimating full probability density functions (PDFs) for both {xHI}{x_HI} and redshift {z}{z} using Bayesian inference with the No-U-Turn Sampler (NUTS), 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 {xHI}{x_HI} and {z}{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 {mFDM 10⁻²²\,eV}{m_FDM approx 10^-22 eV} and {fFDM 0.04}{f_FDM approx 0.04} best match 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.