Learning to Predict the Cosmological Structure Formation (1811.06533v2)

Abstract: Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and employ a large ensemble of computer simulations to compare with the observed data in order to extract the full information of our own Universe. However, to evolve trillions of galaxies over billions of years even with the simplest physics is a daunting task. We build a deep neural network, the Deep Density Displacement Model (hereafter D$^3$M), to predict the non-linear structure formation of the Universe from simple linear perturbation theory. Our extensive analysis, demonstrates that D$^3$M outperforms the second order perturbation theory (hereafter 2LPT), the commonly used fast approximate simulation method, in point-wise comparison, 2-point correlation, and 3-point correlation. We also show that D$^3$M is able to accurately extrapolate far beyond its training data, and predict structure formation for significantly different cosmological parameters. Our study proves, for the first time, that deep learning is a practical and accurate alternative to approximate simulations of the gravitational structure formation of the Universe.

• The paper introduces the Deep Density Displacement Model (D3M) which leverages a U-Net architecture to predict cosmic structure formation with high accuracy.
• The model outperforms traditional methods, reducing point-wise errors and delivering superior two- and three-point correlation function results.
• D3M's ability to generalize across different cosmological parameters suggests it as a computationally efficient alternative to N-body simulations.

Deep Learning for Predicting Cosmological Structure Formation

The research article titled "Learning to Predict the Cosmological Structure Formation" presents a significant advancement in the field of cosmology, specifically in predicting the large-scale structure of the Universe. The paper introduces the Deep Density Displacement Model (D$^3$M), a deep neural network designed to predict cosmological structure formation, offering a novel approach that outperforms traditional methodologies.

Background and Motivation

In cosmology, understanding the evolution of cosmic structures from initial density fluctuations is a fundamental challenge. The cosmological structure formation is a non-linear hierarchical process, leading to complex architectures collectively known as the Cosmic Web. Existing methods like N-body simulations, while effective, are computationally intensive, requiring substantial time and resources to evolve systems of billions of particles over cosmic timescales.

This paper leverages recent advancements in deep learning to provide a computationally efficient alternative to N-body simulations by training a model to predict the non-linear large-scale structure from simpler analytical approximations.

Methods and Model Architecture

The D$^3$M uses a U-Net architecture tailored for volumetric data. The model is trained to map the evolution of matter in the Universe initially approximated by the Zel'dovich Approximation (ZA) to the results of FastPM simulations. FastPM is an approximate N-body simulation that efficiently approaches full N-body accuracy. The researchers opted for the displacement field representation over density fields during training, addressing ambiguities inherent in non-linear density descriptions.

The dataset for training D$^3$M consists of 10,000 simulation pairs, providing extensive coverage and diversity of scenarios under a homogeneous cosmological parameter set.

Results and Evaluation

Several measures were employed to evaluate the performance of D$^3$M, including point-wise error metrics, two-point correlation functions, and three-point correlation functions. The model consistently outperformed the second-order Lagrangian perturbation theory (2LPT) across all these evaluations:

• Point-wise Error: D$^3$M showed a substantial reduction in average relative error compared to 2LPT, indicating enhanced accuracy in particle displacement predictions.
• Two-point Correlation Function: The transfer function and correlation coefficient of the predicted density and displacement fields closely matched the ground truth simulations, particularly at scales $k \lesssim 0.4 \, \text{Mpc}^{-1}$.
• Three-point Correlation Function: The D$^3$M demonstrated superior performance in capturing non-Gaussian features, highlighting its efficacy in modeling complex structure formations.

A noteworthy result is the ability of D$^3$M to extrapolate predictions for cosmological parameters significantly different from those it was trained on, suggesting a robustness and generalization capability that minimizes the need for diverse training datasets.

Implications and Future Directions

The findings illustrate the potential of deep learning models to substitute traditional approximate simulation methods in cosmology, providing accurate and computationally efficient alternatives. The ability of D$^3$M to generalize across different cosmological settings could significantly reduce computational burdens associated with parameter space exploration in cosmic structure studies.

Future work may focus on integrating higher-resolution simulations and extending the model to incorporate more complex physical phenomena to further bridge the gap between approximate and full N-body simulations. Additionally, implementing this approach in real observational data analysis could enhance our capacity to infer cosmic evolution from survey data.

In conclusion, this paper demonstrates a compelling case for harnessing the power of deep learning in cosmology, offering a pathway to accelerate research in understanding the Universe's large-scale structure formation.