Constraining cosmological parameters from N-body simulations with Variational Bayesian Neural Networks

TL;DR

This paper enhances Bayesian Neural Networks with multiplicative normalizing flows to improve the accuracy and calibration of cosmological parameter estimation from astrophysical simulations, outperforming standard methods.

Contribution

It introduces the use of multiplicative normalizing flows in BNNs to better capture complex posterior distributions in cosmological parameter inference.

Findings

MNFs with BNNs outperform standard BNNs in predictive performance.

High accuracy in estimating $\sigma_8$ with $r^2=0.99$.

More realistic and well-calibrated uncertainty estimates.

Abstract

Methods based on Deep Learning have recently been applied on astrophysical parameter recovery thanks to their ability to capture information from complex data. One of these methods is the approximate Bayesian Neural Networks (BNNs) which have demonstrated to yield consistent posterior distribution into the parameter space, helpful for uncertainty quantification. However, as any modern neural networks, they tend to produce overly confident uncertainty estimates and can introduce bias when BNNs are applied to data. In this work, we implement multiplicative normalizing flows (MNFs), a family of approximate posteriors for the parameters of BNNs with the purpose of enhancing the flexibility of the variational posterior distribution, to extract $\Omega_m$, $h$, and $\sigma_8$ from the QUIJOTE simulations. We have compared this method with respect to the standard BNNs, and the flipout estimator. We found that MNFs combined with BNNs outperform the other models obtaining predictive performance with almost one order of magnitude larger that standard BNNs, $\sigma_8$ extracted with high accuracy ($r^2=0.99$), and precise uncertainty estimates. The latter implies that MNFs provide more realistic predictive distribution closer to the true posterior mitigating the bias introduced by the variational approximation and allowing to work with well-calibrated networks.