Constraining cosmological parameters from N-body simulations with variational Bayesian neural networks - Hortúa, Héctor J.; García, Luz Ángela; Castañeda C., Leonardo (Frontiers in Astronomy and Space Sciences, 2023)
Methods based on Deep Learning have recently been applied to recover astrophysical parameters thanks to the ability of these techniques to capture information from complex data. One of these schemes is the approximate Bayesian Neural Networks (BNNs) which has demonstrated to yield a posterior distribution into the parameter space, that is extremely helpful for uncertainty quantification. However, modern neural networks tend to produce overly confident uncertainty estimates and introduce bias when applying BNNs 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 $Ω_m$, $h$, and $σ_8$ from the QUIJOTE simulations. We compared the latter method with respect to the standard BNNs, and the Flipout estimator. We have found that the use of MNFs consistently outperforms the standard BNNs with a percent difference in the Mean Squared Error of 21%, in addition to high accuracy extraction of $σ_8$ ($r^2=0.99$), with precise and consistent uncertainty estimates. The latter implies that MNFs provide a more realistic predictive distribution closer to the true posterior, mitigating the bias introduced by the variational approximation, and allowing us to work with well-calibrated networks.