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Hydrodynamical cosmological simulations are a powerful tool for accuratelypredicting the properties of the intergalactic medium (IGM) and for producingmock skies that can be compared against observational data. However, the needto resolve density fluctuation in the IGM puts a stringent requirement on theresolution of such simulations which in turn limits the volumes which can bemodelled, even on most powerful supercomputers. In this work, we present anovel modeling method which combines physics-driven simulations withdata-driven generative neural networks to produce outputs that arequalitatively and statistically close to the outputs of hydrodynamicalsimulations employing 8 times higher resolution. We show that the Ly-$\alpha$flux field, as well as the underlying hydrodynamic fields, have greatlyimproved statistical fidelity over a low-resolution simulation. Importantly,the design of our neural network allows for sampling multiple realizations froma given input, enabling us to quantify the model uncertainty. Using test data,we demonstrate that this model uncertainty correlates well with the true errorof the Ly-$\alpha$ flux prediction. Ultimately, our approach allows fortraining on small simulation volumes and applying it to much larger ones,opening the door to producing accurate Ly-$\alpha$ mock skies in volumes ofHubble size, as will be probed with DESI and future spectroscopic sky surveys.

Reconstructing Lyman-$\alpha$ Fields from Low-Resolution Hydrodynamical Simulations with Deep Learning