# Cosmic Velocity Field Reconstruction Using AI

**Authors:** Ziyong Wu, Zhenyu Zhang, Shuyang Pan, Haitao Miao, Xin Wang, Cristiano G. Sabiu, Jaime Forero-Romero, Yang Wang, Xiao-Dong Li  
**arXiv:** [2105.09450](https://arxiv.org/abs/2105.09450)  
**Date:** 2021-05-20  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2105.09450v1/

## Key points

- Deep learning technique for inferring non-linear velocity field from dark matter density field
- Utilize U-net style convolutional neural network architecture with 15 convolution layers and 2 deconvolution layers
- Map $32^3$-voxel density field to $20^3$-voxel velocity or momentum fields
- Analyze dark matter simulation with resolution of $2 {h^{-1}}{\rm Mpc}$
- Neural network accurately predicts non-linearity, complexity, and vorticity of velocity and momentum fields
- Captures power spectra value, divergence, and vorticity up to $k\simeq1.4$ $h{\rm Mpc}^{-1}$ with relative error ranging from 1% to $\lesssim$10%
- Neural networks have advantage over perturbation theory in reconstructing velocity or momentum fields
- Deep learning techniques capture complex non-linear relationships between physical quantities
- Dataset and data processing methods discussed in detail
- Construction and architecture of neural network explained
- Findings contribute to understanding cosmic structure formation and have implications for astrophysical applications such as galaxy formation and large-scale structure evolution

## Summary

In this study, we present a deep learning technique for inferring the non-linear velocity field from the dark matter density field. We utilize a U-net style convolutional neural network architecture with 15 convolution layers and 2 deconvolution layers to map the 3-dimensional density field of $32^3$-voxels to the 3-dimensional velocity or momentum fields of $20^3$-voxels. To evaluate our approach's performance, we analyze a dark matter simulation with a resolution of $2 {h^{-1}}{\rm Mpc}$. Our results demonstrate that the neural network is capable of accurately predicting the non-linearity, complexity, and vorticity of the velocity and momentum fields as well as capturing their power spectra value, divergence, and vorticity up to $k\simeq1.4$ $h{\rm Mpc}^{-1}$ with a relative error ranging from 1% to $\lesssim$10%. Comparing our method with perturbation theory reveals that neural networks have an advantage in reconstructing velocity or momentum fields. This highlights the potential superiority of deep learning techniques in capturing complex non-linear relationships between different physical quantities. To provide more context on our work, we discuss our dataset and data processing methods in detail as well as construction and architecture of our neural network. Our findings contribute to advancing our understanding of cosmic structure formation by providing an effective tool for reconstructing velocity fields from dark matter density distributions which has implications for various astrophysical applications such as galaxy formation and large-scale structure evolution.