We propose a fast and accurate methodology for prediction of hydrodynamic gas distributions from Dark Matter N-body simulations. We perform fast emulations of 3D gas density cubes from the Dark Matter counterparts, comparing different Convolutional Neural Network architectures. Our method achieves an accuracy above 95% for the pixel density contrast distributions within the middle regions of the density contrast domain, and 98% accuracy in the matter power spectrum throughout the entire k domain. Moreover, our method provides a gain of 4 orders of magnitude in CPU run times compared to running the full hydrodynamic N-body simulation on a slightly newer computer system. Most importantly, our methodology provides a scalable and generalizable approach to the problem of N-body emulation, with the potential to be applied to simulations of arbitrary sizes and various scalar quantities.

Computations of cosmological properties, such as the density perturbation variance,$\sigma$, are computationally expensive. In this work we propose the application of Symbolic Regression to generate analytical expressions to approximate these quantities. We created simulated data for$\sigma$using a Boltzmann solver, CAMB. These simulations cover seven parameters; the five cosmological parameters and the redshift and mass of dark matter halos. We then apply a Symbolic Regression engine, TuringBot, to this simulated data and obtain an analytical equation to approximate$\sigma$. The resulting mathematical expression has a mean accuracy of ≈ 98.96% over the entire domain, and is five orders of magnitude faster than using simulated data from CAMB, demonstrating the applicability of Symbolic Regression to accelerate cosmological inference.

In this work, we propose an efficient methodology for emulating hydrodynamic gas structures in Dark Matter Nbody simulations. We perform fast emulations of 3D gas density cubes from the Dark Matter counterparts, comparing different machine learning approaches, namely Principal Component Analysis + Random Forest ($\text{PCA}+\text{RF}$) and a Convolutional Neural Network (CNN). The method provides a gain of 5 orders of magnitude in CPU run times compared to running the full hydrodynamic N-body simulation in the same computer system. Using$\text{PCA}+\text{RF}$, the method achieves 98% accuracy in the matter power spectrum compared to the full hydrodynamic simulation throughout most of the k domain$(k < 1.0\ Mpc\ h^{-1})$. Finally, CNNs offer increased accuracy (∼ 99%), showing a striking improvement in performance at the extremes of the k domain.

In this work, we propose a resolution enhancement methodology for discretized scalar fields and apply it to cosmological N-body simulations. We upscale Dark Matter density 3D Eulerian cubes using supervised machine learning and Principal Component Analysis. Once the low-resolution simulation is performed, our methodology doubles its resolution gaining three orders of magnitude in CPU run times compared to performing the full high-resolution simulation in the same computational system. Moreover, we achieve 98% accuracy in the matter power spectrum compared to the full high-resolution simulation throughout most of the k domain$(k < 1.0\ Mpc\ h^{-1})$. Finally, the proposed approach is agnostic to the nature of the simulation field. as long as it corresnonds to a 3D scalar field.

The study of cosmological structure formation usually relies on computationally intensive N-body simulations, that evolve ensembles of particles assuming an underlying physical model. The diversity of physical assumptions and the number of parameters involved often limit the application of these techniques to only a few cases in the multi-dimensional spaces of cosmological parameters. Recently, supervised deep learning methods have been proposed to alleviate part of the computational overhead of N-body methods, but overheads are still high. In this work, we present a new method, based on Functional Principal Component Analysis (FPCA), that allows fast and accurate estimations of 3D N-body density fields and run-time gains of orders of magnitude when compared with traditional N-body simulations of the same resolution. Here we also compare FPCA to an approach of compressing the simulations through Principal Component Analysis (PCA) and using a single-layer Neural Network (NN) to perform the emulation. We show that FPCA can achieve slightly better accuracy than the PCA+NN method, short-cutting the need to apply supervised learning as an additional step in the emulation of cosmological simulations.