  We explore the use of Deep Learning to infer physical quantities from the
observable transmitted flux in the Lyman-alpha forest. We train a Neural
Network using redshift z=3 outputs from cosmological hydrodynamic simulations
and mock datasets constructed from them. We evaluate how well the trained
network is able to reconstruct the optical depth for Lyman-alpha forest
absorption from noisy and often saturated transmitted flux data. The Neural
Network outperforms an alternative reconstruction method involving log
inversion and spline interpolation by approximately a factor of 2 in the
optical depth root mean square error. We find no significant dependence in the
improvement on input data signal to noise, although the gain is greatest in
high optical depth regions. The Lyman-alpha forest optical depth studied here
serves as a simple, one dimensional, example but the use of Deep Learning and
simulations to approach the inverse problem in cosmology could be extended to
other physical quantities and higher dimensional data.
