A Physics Informed Bayesian Neural Network for the Neutron Star Equation of State

Abstract

We present a physics-informed Bayesian neural-network framework for inferring neutron-star equations of state from theoretical priors and propagating the resulting uncertainty to stellar observables. Trained on a representative set of hadronic EoSs, the model learns the equation of state through stochastic variational inference by representing the squared speed of sound with a bounded network output and obtaining the pressure by integration, so that causality, thermodynamic stability, and monotonicity are guaranteed by construction, with low-density nuclear and perturbative-QCD normalization anchors. Core EoSs are matched to an SLy4 crust and propagated through a unified Tolman-Oppenheimer-Volkoff-plus-tidal solver to obtain posterior predictions in the mass-radius ($M$-$R$) and mass-tidal-deformability ($M$-$\Lambda$) planes. The physics-informed prior is then updated with current multi-messenger data: NICER radius measurements, the GW170817 tidal-deformability constraint, and the $2M_{\odot }$ maximum-mass bound; included directly in the variational objective. The observational update moves the canonical radius from $R_{1.4}=13.41\mathrm{km}$ in the prior to $R_{1.4}=12.74_{-0.73}^{+0.97}\mathrm{km}$ (nominal 90\% variational CI), with ${\Lambda }_{1.4}=428_{-130}^{+249}$ and $M_{\max }\gtrsim 2.0M_{\odot }$. This framework provides a non-parametric route from microphysical EoS uncertainty to neutron-star observables.

Accepted in PRD