LyAl-Net: A high-efficiency Lyman-$\alpha$ forest simulation with a neural network

The inference of cosmological quantities requires accurate and large hydrodynamical cosmological simulations. Unfortunately, their computational time can take millions of CPU hours for a modest coverage in cosmological scales ($\approx (100 {h^{-1}}\,\text{Mpc})^3)$). The possibility to generate large quantities of mock Lyman-$\alpha$ observations opens up the possibility of much better control on covariance matrices estimate for cosmological parameters inference, and on the impact of systematics due to baryonic effects. We present a machine learning approach to emulate the hydrodynamical simulation of intergalactic medium physics for the Lyman-$\alpha$ forest called LyAl-Net. The main goal of this work is to provide highly efficient and cheap simulations retaining interpretation abilities about the gas field level, and as a tool for other cosmological exploration. We use a neural network based on the U-net architecture, a variant of convolutional neural networks, to predict the neutral hydrogen physical properties, density, and temperature. We train the LyAl-Net model with the Horizon-noAGN simulation, though using only 9% of the volume. We also explore the resilience of the model through tests of a transfer learning framework using cosmological simulations containing different baryonic feedback. We test our results by analysing one and two-point statistics of emulated fields in different scenarios, as well as their stochastic properties. The ensemble average of the emulated Lyman-$\alpha$ forest absorption as a function of redshift lies within 2.5% of one derived from the full hydrodynamical simulation. The computation of individual fields from the dark matter density agrees well with regular physical regimes of cosmological fields. The results tested on IllustrisTNG100 showed a drastic improvement in the Lyman-$\alpha$ forest flux without arbitrary rescaling.