Learning to Predict the Cosmological Structure Formation

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.Comment: 8 pages, 5 figures, 1 tabl

Extracting cosmological parameters from N-body simulations using machine learning techniques

We make use of snapshots taken from the Quijote suite of simulations, consisting of 2000 simulations where five cosmological parameters have been varied ($\Omega_m$, $\Omega_b$, $h$, $n_s$ and $\sigma_8$) in order to investigate the possibility of determining them using machine learning techniques. In particular, we show that convolutional neural networks can be employed to accurately extract $\Omega_m$ and $\sigma_8$ from the N-body simulations, and that these parameters can also be found from the non-linear matter power spectrum obtained from the same suite of simulations using both random forest regressors and deep neural networks. We show that the power spectrum provides competitive results in terms of accuracy compared to using the simulations and that we can also estimate the scalar spectral index $n_s$ from the power spectrum, at a lower precision.Comment: 11 pages, 5 figure