Mean-Field Simulation-Based Inference for Cosmological Initial Conditions

TL;DR

This paper introduces a fast, Bayesian field reconstruction method for cosmological initial conditions that models the posterior as a diagonal Gaussian in Fourier space, enabling rapid training and sampling.

Contribution

It presents a novel, efficient approach for reconstructing cosmological initial conditions using a trainable Gaussian model compatible with standard N-body simulators.

Findings

Training takes about 1 hour on GPU

Sampling is under 3 seconds for 1000 samples

Reconstructed initial conditions match summary statistics

Abstract

Reconstructing cosmological initial conditions (ICs) from late-time observations is a difficult task, which relies on the use of computationally expensive simulators alongside sophisticated statistical methods to navigate multi-million dimensional parameter spaces. We present a simple method for Bayesian field reconstruction based on modeling the posterior distribution of the initial matter density field to be diagonal Gaussian in Fourier space, with its covariance and the mean estimator being the trainable parts of the algorithm. Training and sampling are extremely fast (training: $\sim 1 \, \mathrm{h}$ on a GPU, sampling: $\lesssim 3 \, \mathrm{s}$ for 1000 samples at resolution $128^3$), and our method supports industry-standard (non-differentiable) $N$-body simulators. We verify the fidelity of the obtained IC samples in terms of summary statistics.