DeepVoid: A Deep Learning Void Detector

TL;DR

DeepVoid is presented, an application of deep learning trained on a physical definition of cosmic voids to detect voids in density fields and galaxy distributions to detect voids in density fields and galaxy distributions.

Abstract

We present DeepVoid, an application of deep learning trained on a physical definition of cosmic voids to detect voids in density fields and galaxy distributions. By semantically segmenting the IllustrisTNG simulation volume using the tidal tensor, we train a deep convolutional neural network to classify local structure using a U-Net architecture for training and prediction. The model achieves a void F1 score of 0.96 and a Matthews correlation coefficient over all structural classes of 0.81 for dark matter particles in IllustrisTNG with interparticle spacing of $λ=0.33 h^{-1} \text{Mpc}$. We then apply the machine learning technique of curricular learning to enable the model to classify structure in data with significantly larger intertracer separation. At the highest tracer separation tested, $λ=10 h^{-1} \text{Mpc}$, the model achieves a void F1 score of 0.89 and a Matthews correlation coefficient of 0.6 on IllustrisTNG subhalos.

Figures (9)

• Figure 1: Left: TNG300-3-Dark mass density contrast defined as $\delta(\Vec{x})=\rho(\Vec{x})/{\Bar{\rho}}-1$, where $\Bar{\rho}$ is the average matter density in the volume. Center: corresponding gravitational potential $\Phi$. Note that both $\delta$ and $\Phi$ have been scaled and shifted such that their minimum value is zero and their standard deviation is one, and their logarithm plotted for ease of interpretability. Right: multilabel tidal tensor classified mask. This mask is our "truth table" for training. These plots are one slice thick, with $N_{\rm mesh}=512$, so they are 0.4 $h^{-1}$ Mpc thick.
• Figure 2: A comparison of different eigenvalue thresholds used to create a tidal-tensor-based map of structural morphology in TNG300-3-Dark. Top left:$\lambda_\mathrm{th}=0$; Top right:$\lambda_\mathrm{th}=0.3$; Bottom left:$\lambda_\mathrm{th}=0.65$ (our default); Bottom right:$\lambda_\mathrm{th}=1$. The morphology of the cosmic web as defined by $\lambda_\mathrm{th}$$=0$ consists of tiny isolated voids surrounded by huge amounts of wall voxels. We see a more realistic depiction of the Universe's large-scale structure at slightly positive values of $\lambda_\mathrm{th}$.
• Figure 3: Schematic of a U-Net architecture with three levels of resolution ('depth'). In (a), chunks of a density field are fed through the successive layers in (b), with cubes representing 3D feature maps colored orange on the encoding side, and green on the decoding side. Numbers next to the curly brackets indicate the size of the activation images in a given layer, while numbers next to the vertical ellipses indicate the number of filters in each layer. Colored arrows indicate operations performed between different layers. Horizontal gray arrows represent the merging of feature maps used to transfer small-scale spatial information from the encoding layers to the decoding layers. Without these concatenations, the U-Net architecture is identical to that of an autoencoder. The predicted structural segmentation is shown in (c).
• Figure 4: Metrics during the training of a DeepVoid base model. Upper: SCCE loss vs. training epochs. Lower: Matthews correlation coefficient for training and testing datasets during training. Note that while around epoch 40 the training and validation scores begin to diverge we further monitor the validation loss to stop training when it does not improve for 25 epochs.
• Figure 5: Upper row: TNG mass density contrast and prediction for the best base TNG model predicting on the full TNG particle distribution with $\lambda=0.33$$h^{-1}$ Mpc. Upper right panel is the tidal tensor truth table, which is the same for all models. Lower row: TNG subhalo positions and prediction for the best CL model. Subhalos are first ordered by mass, then abundance matched such that the average intertracer separation is $\lambda=10$$h^{-1}$ Mpc. Subhalos that are within 2 $h^{-1}$ Mpc of either side of the slice taken through the simulation are shown. The base model was trained on the TNG full density with a U-Net with three layers of depth and 32 initial filters. The model was then curriculum-trained on subhalos with $\lambda=3$$h^{-1}$ Mpc average spacing and then curriculum-trained again out to $\lambda=10$$h^{-1}$ Mpc. While the slices through the prediction cubes necessarily include voxels in both the training and validation data, only the validation data are used to compute performance metrics reported in this paper.