Neural network maps cosmic voids, walls and filaments from sparse galaxy tracers

The work

Technical · from the record

DeepVoid trains a three-dimensional U-Net to reproduce a tidal-tensor classification of the IllustrisTNG300-3-Dark volume into void, wall, filament and halo voxels, using the tidal tensor computed from the full dark matter density field as the training labels. On the full dark matter particle density field, with interparticle spacing of 0.33 h−1 Mpc, the best model reached a void F1 score of 0.96 and a Matthews correlation coefficient of 0.81 on validation data. Curriculum learning, in which encoder weights from the dense-field model were frozen and the rest retrained on progressively sparser subhalo density fields, gave a void F1 score of 0.89 and an MCC of 0.60 at an intertracer spacing of 10 h−1 Mpc, compared with a void F1 of 0.89 and an MCC of 0.56 for a model trained directly on that sparse field. Wall classification degraded across this range, with the proportion of wall voxels classified as void rising from 14% to 31%.

How AI was used

Voxel-wise structural labels were computed without machine learning, by cloud-in-cell binning of the dark matter particles of the TNG300-3-Dark z=0 snapshot onto a 512^3 grid, solving Poisson's equation by fast Fourier transform, smoothing the potential to an effective scale of 1 h−1 Mpc, taking the Hessian of the potential and counting eigenvalues above a threshold of 0.65 to assign void, wall, filament or halo. These labels served as the training target for a 3D U-Net built in Keras on TensorFlow, with (3,3,3) convolution kernels, ReLU activations, MaxPooling3D downsampling, encoder-to-decoder concatenations, batch normalisation in every other block, a softmax output over four classes and argmax class assignment. Density and label fields were cut into 128^3 subcubes, min-max scaled, augmented by three 90-degree rotations, split 80/20 into training and validation sets and shuffled. Models were trained with sparse categorical cross entropy using Adam at an initial learning rate of 0.0003, a scheduler quartering the rate after 15 epochs without validation-loss improvement, early stopping after 25 such epochs and retention of the lowest-validation-loss weights; focal loss and Dice/SCCE combinations were also tried. Sparse tracer fields were built by ranking subhalos by virial mass and selecting enough of the most massive to reach target intertracer separations of 1, 3, 5, 7 and 10 h−1 Mpc, then cloud-in-cell binning them while keeping labels derived from the full density field. To handle sparsity, curriculum learning transferred base-model weights to sparser fields under several encoder-freezing schemes, including a two-step scheme passing through an intermediate separation. Prediction was performed on half-overlapping 128^3 subcubes in batches of eight, with only central regions retained on reassembly, and evaluated with confusion matrices, balanced accuracy, micro-averaged F1, void F1, MCC and precision-recall curves, plus a test on the volume rotated by 45 degrees with the mask recomputed.