Bayesian Nonparametric Inference of the Neutron Star Equation of State via a Neural Network

We develop a new nonparametric method to reconstruct the Equation of State (EoS) Neutron Star with multimessenger data. As an universal function approximator, Feed-Forward Neural Network (FFNN) one hidden layer and sigmoidal activation can approximately fit any continuous function. Thus we are able implement FFNN representation EoSs. This is validated by its capabilities fitting theoretical EoSs recovering injected parameters. Then adopt this analyze real data, including mass-tidal deformability measurement from Binary (BNS) merger Gravitational Wave (GW) event GW170817 mass-radius PSR J0030+0451 {\it NICER}. take publicly available samples construct likelihood use nested sampling obtain posteriors parameters according Bayesian theorem, which in turn be translated EoS Combining all these for canonical 1.4 $M_\odot$ neutron star, get radius $R_{1.4}=11.83^{+1.25}_{-1.08}$ km tidal $\Lambda_{1.4} = 323^{+334}_{-165}$ (90\% confidence interval).Furthermore, find that high density region ($\geq 3\rho_{\rm sat}$), 90\% lower limits $c_{\rm s}^2/c^2$ ($c_{\rm s}$ sound speed $c$ velocity light vacuum) above $1/3$, means so-called conformal limit (i.e., s}^2/c^2<1/3$) not always valid stars.