Classifying the Large Scale Structure of the Universe with Deep Neural
  Networks
  We present the first application of deep neural networks to the semantic
segmentation of cosmological filaments and walls in the Large Scale Structure
of the Universe. Our results are based on a deep Convolutional Neural Network
(CNN) with a U-Net architecture trained using an existing state-of-the-art
manually-guided segmentation method. We successfully trained an tested an U-Net
with a Voronoi model and an N-body simulation. The predicted segmentation masks
from the Voronoi model have a Dice coefficient of 0.95 and 0.97 for filaments
and mask respectively. The predicted segmentation masks from the N-body
simulation have a Dice coefficient of 0.78 and 0.72 for walls and filaments
respectively. The relatively lower Dice coefficient in the filament mask is the
result of filaments that were predicted by the U-Net model but were not present
in the original segmentation mask.
  Our results show that for a well-defined dataset such as the Voronoi model
the U-Net has excellent performance. In the case of the N-body dataset the
U-Net produced a filament mask of higher quality than the segmentation mask
obtained from a state-of-the art method. The U-Net performs better than the
method used to train it, being able to find even the tenuous filaments that the
manually-guided segmentation failed to identify.
  The U-Net presented here can process a $512^3$ volume in a few minutes and
without the need of complex pre-processing. Deep CNN have great potential as an
efficient and accurate analysis tool for the next generation large-volume
computer N-body simulations and galaxy surveys.
