Fast Sampling of Cosmological Initial Conditions with Gaussian Neural Posterior Estimation

2025-02-05

AI Summary

To address the high-dimensional, nonlinear inverse problem of reconstructing the primordial dark matter density field from late-time cosmological observations, this paper introduces a novel simulation-based inference (SBI) framework. Our method leverages non-differentiable N-body simulations and operates efficiently on a single GPU. Key contributions include: (i) the first construction of a diagonal Gaussian posterior model in Fourier space, enabling millisecond-scale single-sample generation; (ii) an analytic, wavenumber-dependent covariance fitting technique that seamlessly upgrades any point estimator into an efficient posterior sampler without loss of fidelity. The framework achieves数千 samples per second—accelerating state-of-the-art methods by several orders of magnitude. Rigorous validation via summary statistics and Bayesian consistency tests confirms both statistical reliability and physical fidelity of the generated posterior samples.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Reconstruct primordial matter density field efficiently.
• Use Gaussian posterior estimation for cosmological simulations.
• Enable fast sampling with non-differentiable simulators.

Innovation

• Gaussian Neural Posterior Estimation
• Simulation-based inference
• Fast sampling with GPU