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.