Fast Sampling of Cosmological Initial Conditions with Gaussian Neural Posterior Estimation

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.

Tests for model misspecification in simulation-based inference: from local distortions to global model checks

Model misspecification analysis strategies, such as anomaly detection, model validation, and model comparison are a key component of scientific model development. Over the last few years, there has been a rapid rise in the use of simulation-based inference (SBI) techniques for Bayesian parameter estimation, applied to increasingly complex forward models. To move towards fully simulation-based analysis pipelines, however, there is an urgent need for a comprehensive simulation-based framework for model misspecification analysis. In this work, we provide a solid and flexible foundation for a wide range of model discrepancy analysis tasks, using distortion-driven model misspecification tests. From a theoretical perspective, we introduce the statistical framework built around performing many hypothesis tests for distortions of the simulation model. We also make explicit analytic connections to classical techniques: anomaly detection, model validation, and goodness-of-fit residual analysis. Furthermore, we introduce an efficient self-calibrating training algorithm that is useful for practitioners. We demonstrate the performance of the framework in multiple scenarios, making the connection to classical results where they are valid. Finally, we show how to conduct such a distortion-driven model misspecification test for real gravitational wave data, specifically on the event GW150914.

Mean-Field Simulation-Based Inference for Cosmological Initial Conditions

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.

Bayesian Simulation-based Inference for Cosmological Initial Conditions

Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to observations are readily available for many applications. We present a versatile Bayesian field reconstruction algorithm rooted in simulation-based inference and enhanced by autoregressive modeling. The proposed technique is applicable to generic (non-differentiable) forward simulators and allows sampling from the posterior for the underlying field. We show first promising results on a proof-of-concept application: the recovery of cosmological initial conditions from late-time density fields.