Cosmic Velocity Field Reconstruction Using Ai

We develop a deep-learning technique to infer the nonlinear velocity field from the dark matter density field. The deep-learning architecture we use is a "U-net" style convolutional neural network, which consists of 15 convolution layers and 2 deconvolution layers. This setup maps the three-dimensional density field of 32(3) voxels to the three-dimensional velocity or momentum fields of 20(3) voxels. Through the analysis of the dark matter simulation with a resolution of 2h (-1) Mpc, we find that the network can predict the the nonlinearity, complexity, and vorticity of the velocity and momentum fields, as well as the power spectra of their value, divergence, and vorticity and its prediction accuracy reaches the range of k similar or equal to 1.4 h Mpc(-1) with a relative error ranging from 1% to less than or similar to 10%. A simple comparison shows that neural networks may have an overwhelming advantage over perturbation theory in the reconstruction of velocity or momentum fields.