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ABSTRACT We explore the use of Deep Learning to infer physical quantities from the observable transmitted flux in the Ly α forest. We train a Neural Network using redshift z = 3 outputs from cosmological hydrodynamic simulations and mock data sets constructed from them. We evaluate how well the trained network is able to reconstruct the optical depth for Ly α 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 Ly α 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.