Fast Sampling of Cosmological Initial Conditions with Gaussian Neural Posterior Estimation

TL;DR

This paper introduces a fast, simulation-efficient method using Gaussian neural posterior estimation to generate cosmological initial condition samples from late-time observations, significantly accelerating the process for high-resolution dark matter simulations.

Contribution

The authors develop a novel SBI approach that models the posterior as Gaussian with diagonal covariance in Fourier space, enabling rapid sampling of initial conditions from complex cosmological simulations.

Findings

Samples generated within seconds on a single GPU

Method is applicable to high-resolution N-body simulations

Validated samples match true initial conditions using statistical tests

Abstract

Knowledge of the primordial matter density field from which the large-scale structure of the Universe emerged over cosmic time is of fundamental importance for cosmology. However, reconstructing these cosmological initial conditions from late-time observations is a notoriously difficult task, which requires advanced cosmological simulators and sophisticated statistical methods to explore a multi-million-dimensional parameter space. We show how simulation-based inference (SBI) can be used to tackle this problem and to obtain data-constrained realisations of the primordial dark matter density field in a simulation-efficient way with general non-differentiable simulators. Our method is applicable to full high-resolution dark matter $N$-body simulations and is based on modelling the posterior distribution of the constrained initial conditions to be Gaussian with a diagonal covariance matrix in Fourier space. As a result, we can generate thousands of posterior samples within seconds on a single GPU, orders of magnitude faster than existing methods, paving the way for sequential SBI for cosmological fields. Furthermore, we perform an analytical fit of the estimated dependence of the covariance on the wavenumber, effectively transforming any point-estimator of initial conditions into a fast sampler. We test the validity of our obtained samples by comparing them to the true values with summary statistics and performing a Bayesian consistency test.