LyαNNA: A deep learning field-level inference machine for the Lyman-α forest

The inference of astrophysical and cosmological properties from the Lyman-alpha forest conventionally relies on summary statistics of the transmission field that carry useful but limited information. We present a deep learning framework for inference from the Lyman-alpha forest at the field level. This framework consists of a 1D residual convolutional neural network (ResNet) that extracts spectral features and performs regression on thermal parameters of the intergalactic medium that characterize the power-law temperature-density relation. We trained this supervised machinery using a large set of mock absorption spectra from Nyx hydrodynamic simulations at $z=2.2$ with a range of thermal parameter combinations (labels). We employed Bayesian optimization to find an optimal set of hyperparameters for our network, and then employed a committee of 20 neural networks for increased statistical robustness of the network inference. In addition to the parameter point predictions, our machine also provides a self-consistent estimate of their covariance matrix with which we constructed a pipeline for inferring the posterior distribution of the parameters. We compared the results of our framework with the traditional summary based approach, namely the power spectrum and the probability density function (PDF) of transmission, in terms of the area of the 68 credibility regions as our figure of merit (FoM). In our study of the information content of perfect (noise- and systematics-free) lya forest spectral datasets, we find a significant tightening of the posterior constraints --- factors of 10.92 and 3.30 in FoM over the power spectrum only and jointly with PDF, respectively --- which is the consequence of recovering the relevant parts of information that are not carried by the classical summary statistics.