Mean-Field Simulation-Based Inference for Cosmological Initial Conditions
This addresses the challenge of computationally expensive simulations in cosmology, offering a fast and efficient solution for researchers in astrophysics and cosmology, though it appears incremental as it builds on existing statistical methods with a simplified model.
The paper tackles the problem of reconstructing cosmological initial conditions from late-time observations by introducing a fast Bayesian field reconstruction method that models the posterior as a diagonal Gaussian in Fourier space, achieving training in about 1 hour on a GPU and sampling 1000 samples in under 3 seconds at 128^3 resolution.
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.