Bayesian Inference of Primordial Magnetic Field Parameters from CMB with Spherical Graph Neural Networks

TL;DR

This paper introduces a Bayesian graph deep learning framework using spherical CNNs to estimate primordial magnetic field parameters from CMB maps, providing accurate predictions with uncertainty quantification.

Contribution

It presents a novel DeepSphere-Bayesian Neural Network approach for cosmological parameter estimation directly from spherical CMB data, incorporating uncertainty quantification.

Findings

Achieved $R^{2}$ scores over 0.89 for magnetic parameter estimation.

Provided well-calibrated uncertainty estimates via post-hoc training techniques.

Demonstrated robust and accurate parameter inference from simulated CMB maps.

Abstract

Deep learning has emerged as a transformative methodology in modern cosmology, providing powerful tools to extract meaningful physical information from complex astronomical datasets. This paper implements a novel Bayesian graph deep learning framework for estimating key cosmological parameters in a primordial magnetic field (PMF) cosmology directly from simulated Cosmic Microwave Background (CMB) maps. Our methodology utilizes DeepSphere, a spherical convolutional neural network architecture specifically designed to respect the spherical geometry of CMB data through HEALPix pixelization. To advance beyond deterministic point estimates and enable robust uncertainty quantification, we integrate Bayesian Neural Networks (BNNs) into the framework, capturing aleatoric and epistemic uncertainties that reflect the model confidence in its predictions. The proposed approach demonstrates exceptional performance, achieving $R^{2}$ scores exceeding 0.89 for the magnetic parameter estimation. We further obtain well-calibrated uncertainty estimates through post-hoc training techniques including Variance Scaling and GPNormal. This integrated DeepSphere-BNNs framework not only delivers accurate parameter estimation from CMB maps with PMF contributions but also provides reliable uncertainty quantification, providing the necessary tools for robust cosmological inference in the era of precision cosmology.