Learning to Predict the Cosmological Structure Formation
  Matter evolved under influence of gravity from minuscule density
fluctuations. Non-perturbative structure formed hierarchically over all scales,
and developed non-Gaussian features in the Universe, known as the Cosmic Web.
To fully understand the structure formation of the Universe is one of the holy
grails of modern astrophysics. Astrophysicists survey large volumes of the
Universe and employ a large ensemble of computer simulations to compare with
the observed data in order to extract the full information of our own Universe.
However, to evolve trillions of galaxies over billions of years even with the
simplest physics is a daunting task. We build a deep neural network, the Deep
Density Displacement Model (hereafter D$^3$M), to predict the non-linear
structure formation of the Universe from simple linear perturbation theory. Our
extensive analysis, demonstrates that D$^3$M outperforms the second order
perturbation theory (hereafter 2LPT), the commonly used fast approximate
simulation method, in point-wise comparison, 2-point correlation, and 3-point
correlation. We also show that D$^3$M is able to accurately extrapolate far
beyond its training data, and predict structure formation for significantly
different cosmological parameters. Our study proves, for the first time, that
deep learning is a practical and accurate alternative to approximate
simulations of the gravitational structure formation of the Universe.
