Fast emulation of cosmological density fields based on dimensionality reduction and supervised machine learning

¹ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
e-mail: mjconceicao@ciencias.ulisboa.pt
² Instituto de Astrofísica e Ciências do Espacço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
³ Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA 92697, USA
⁴ CENTRA, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
⁵ Departamento de Física, ETSI Navales, Universidad Politécnica de Madrid, Avda. de la Memoria 4, 28040 Madrid, Spain

Received: 24 April 2023
Accepted: 21 August 2023

Abstract

N-body simulation is the most powerful method for studying the nonlinear evolution of large-scale structures. However, these simulations require a great deal of computational resources, making their direct adoption unfeasible in scenarios that require broad explorations of parameter spaces. In this work we show that it is possible to perform fast dark matter density field emulations with competitive accuracy using simple machine learning approaches. We built an emulator based on dimensionality reduction and machine learning regression combining simple principal component analysis and supervised learning methods. For the estimations with a single free parameter we trained on the dark matter density parameter, Ω_m, while for emulations with two free parameters we trained on a range of Ω_m and redshift. The method first adopts a projection of a grid of simulations on a given basis. Then, a machine learning regression is trained on this projected grid. Finally, new density cubes for different cosmological parameters can be estimated without relying directly on new N-body simulations by predicting and de-projecting the basis coefficients. We show that the proposed emulator can generate density cubes at nonlinear cosmological scales with density distributions within a few percent compared to the corresponding N-body simulations. The method enables gains of three orders of magnitude in CPU run times compared to performing a full N-body simulation while reproducing the power spectrum and bispectrum within ∼1% and ∼3%, respectively, for the single free parameter emulation and ∼5% and ∼15% for two free parameters. This can significantly accelerate the generation of density cubes for a wide variety of cosmological models, opening doors to previously unfeasible applications, for example parameter and model inferences at full survey scales, such as the ESA/NASA Euclid mission.