Uncertainty-Aware Deep Learning for the Ly$α$ Forest: CNN-Based Absorber Detection and Characterization

The Ly$\alpha$ forest is a powerful probe of the intergalactic medium and small-scale matter distribution, but deriving absorber properties traditionally requires computationally expensive Voigt-profile fitting. We present a convolutional neural network (CNN) that identifies and characterizes H I Ly$\alpha$ absorbers directly from quasar spectra. The model is trained on synthetic spectra generated from the IllustrisTNG simulation and fitted with the VIPER Voigt-profile fitting code to provide training labels. The network simultaneously predicts absorber presence, column density ($N_{\rm HI}$), Doppler parameter ($b_{\rm HI}$), and line centroid. On simulated spectra, the CNN achieves an F1 score of $\sim$0.8, with mean absolute errors of $\sim$0.18 in $\log N_{\rm HI}$ and $\sim$0.10 in $\log b_{\rm HI}$. It accurately reproduces the H I column density distribution function (CDDF) and the $b_{\rm HI}$--$N_{\rm HI}$ relation, recovering CDDF slopes consistent with VIPER and a lower-envelope relation with an RMS difference of only 0.36 km s$^{-1}$. Applied to high-resolution UVES spectra, performance decreases to an F1 score of $\sim$0.5, with mean absolute errors of $\sim$0.34 in $\log N_{\rm HI}$ and $\sim$0.21 in $\log b_{\rm HI}$. Latent-space analysis reveals a significant domain shift between the simulated and observational spectra, contributing to the reduced performance. Nevertheless, the CNN preserves the observed CDDF and $b_{\rm HI}$--$N_{\rm HI}$ distributions, yielding CDDF slopes consistent with VIPER and a lower-envelope RMS difference of 2.96 km s$^{-1}$. Monte Carlo dropout is implemented during inference to quantify predictive uncertainties. Together with its computational efficiency, the method provides a scalable and uncertainty-aware framework for Ly$\alpha$ forest analysis in upcoming spectroscopic surveys.