Cosmological parameter estimation from large-scale structure deep
  learning
  We propose a light-weight deep convolutional neural network (CNN) to estimate
the cosmological parameters from simulated 3-dimensional dark matter
distributions with high accuracy. The training set is based on 465 realizations
of a cubic box with a side length of $256\ h^{-1}\ \rm Mpc$, sampled with
$128^3$ particles interpolated over a cubic grid of $128^3$ voxels. These
volumes have cosmological parameters varying within the flat $\Lambda$CDM
parameter space of $0.16 \leq \Omega_m \leq 0.46$ and $2.0 \leq 10^9 A_s \leq
2.3$. The neural network takes as an input cubes with $32^3$ voxels and has
three convolution layers, three dense layers, together with some batch
normalization and pooling layers. In the final predictions from the network we
find a $2.5\%$ bias on the primordial amplitude $\sigma_8$ that can not easily
be resolved by continued training. We correct this bias to obtain unprecedented
accuracy in the cosmological parameter estimation with statistical
uncertainties of $\delta \Omega_m$=0.0015 and $\delta \sigma_8$=0.0029, which
are several times better than the results of previous CNN works. Compared with
a 2-point analysis method using clustering region of 0-130 and 10-130 $h^{-1}$
Mpc, the CNN constraints are several times and an order of magnitude more
precise, respectively. Finally, we conduct preliminary checks of the
error-tolerance abilities of the neural network, and find that it exhibits
robustness against smoothing, masking, random noise, global variation,
rotation, reflection, and simulation resolution. Those effects are well
understood in typical clustering analysis, but had not been tested before for
the CNN approach. Our work shows that CNN can be more promising than people
expected in deriving tight cosmological constraints from the cosmic large scale
structure.
