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Mean-Field Simulation-Based Inference for Cosmological Initial Conditions (2410.15808v1)

Published 21 Oct 2024 in astro-ph.CO, astro-ph.IM, and cs.LG

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 $1283$), 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.

Summary

  • The paper introduces a Bayesian field reconstruction method that models initial conditions as a Gaussian in Fourier space.
  • It employs simulation-based inference with a diagonal likelihood covariance, enabling efficient, non-differentiable N-body sampling.
  • Validation with Quijote simulations confirms high large-scale accuracy, endorsing its potential for extended observational cosmology.

Mean-Field Simulation-Based Inference for Cosmological Initial Conditions

The paper introduces a novel method for reconstructing cosmological initial conditions (ICs) from late-time observations, a complex task due to the non-linear nature of cosmic evolution. The authors propose a Bayesian inference approach, utilizing simulation-based inference (SBI) to efficiently navigate the high-dimensional parameter space inherent in cosmological data.

Methodology

The core contribution of the paper is a Bayesian field reconstruction technique that models the posterior distribution of the initial matter density field as a Gaussian in Fourier space. This approach leverages the fact that early-universe fluctuations can be described accurately by Gaussian random fields. The method focuses on two main trainable components: the maximum a-posteriori (MAP) estimator and the likelihood covariance matrix, both diagonal in Fourier space. The estimation and sampling processes are computationally efficient, requiring minimal time due to the diagonal Gaussian assumption.

The forward model is based on NN-body simulations, which do not need to be differentiable, thus allowing the use of industry-standard cosmological codes. The training involves optimizing a neural network-based MAP estimator along with the likelihood precision matrix in a way that captures both linear and non-linear cosmic structure growth.

Results and Validation

The authors verify the model using data from the Quijote NN-body simulations, showing that the reconstructed ICs are statistically consistent with the true posterior distribution. The power spectrum, transfer function, and cross-correlation metrics demonstrate high accuracy, especially in the large-scale regime. A Bayesian coverage test confirms that the sample posterior is indeed representative of true posterior variability.

Implications and Future Work

This method provides significant practical benefits due to its speed and simplicity, offering near-instantaneous sampling capabilities ideal for large datasets. Beyond its immediate application to 3D matter overdensities, the framework is inherently adaptable to include additional observational complications such as biased tracers or survey effects, highlighting its potential utility in observational cosmology.

Looking ahead, a promising direction involves integrating cosmological parameter inference with the IC reconstruction, potentially employing sequential SBI techniques for enhanced parameter marginalization. Furthermore, while the Gaussian diagonal approximation has proven effective for the current scale, extending into smaller scales may require more sophisticated modeling strategies.

Conclusion

The proposed mean-field SBI-based technique stands out for its computational efficiency and effectiveness in reconstructing cosmological ICs. It opens avenues for applying advanced probabilistic methods to complex astrophysical datasets, marking a forward step in leveraging machine learning to solve intricate cosmological problems.

This framework is valuable for researchers in computational cosmology seeking to bridge forward simulation models with backward inference tasks, providing a robust methodology to explore the universe's initial conditions.

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