  Reconstructing the Gaussian initial conditions at the beginning of the
Universe from the survey data in a forward modeling framework is a major
challenge in cosmology. This requires solving a high dimensional inverse
problem with an expensive, non-linear forward model: a cosmological N-body
simulation. While intractable until recently, we propose to solve this
inference problem using an automatically differentiable N-body solver, combined
with a recurrent networks to learn the inference scheme and obtain the
maximum-a-posteriori (MAP) estimate of the initial conditions of the Universe.
We demonstrate using realistic cosmological observables that learnt inference
is 40 times faster than traditional algorithms such as ADAM and LBFGS, which
require specialized annealing schemes, and obtains solution of higher quality.
