  We introduce the Python program THALAS (TensorFlow Hydrodynamics Analysis for
Lyman-Alpha Simulations), which maps baryon fields (baryon density,
temperature, and velocity) to Ly$\alpha$ optical depth fields in both real
space and redshift space. Unlike previous Ly$\alpha$ codes, THALAS is fully
differentiable, enabling a wide variety of potential applications for general
analysis of hydrodynamical simulations and cosmological inference. To
demonstrate THALAS's capabilities, we apply it to the Ly$\alpha$ forest
inversion problem: given a Ly$\alpha$ optical depth field, we reconstruct the
corresponding real-space dark matter density field. Such applications are
relevant to both cosmological and three-dimensional tomographic analyses of
Lyman Alpha forest data.
