Nonparametric Representation of Neutron Star Equation of State Using Variational Autoencoder

Abstract

We introduce a new nonparametric representation of the neutron star (NS) equation of state (EOS) by using the variational autoencoder (VAE). As a deep neural network, the VAE is frequently used for dimensionality reduction since it can compress input data to a low-dimensional latent space using the encoder component and then reconstruct the data using the decoder component. Once a VAE is trained, one can take the decoder of the VAE as a generator. We employ 100,000 EOSs that are generated using the nonparametric representation method based on Han et al. as the training set and try different settings of the neural network, then we get an EOS generator (the trained VAE’s decoder) with four parameters. We use the mass–tidal-deformability data of binary NS merger event GW170817, the mass–radius data of PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, and 4U 1702-429, and the nuclear constraints to perform the Bayesian inference. The overall results of the analysis that includes all the observations are ${R}_{1.4}={12.59}_{-0.42}^{+0.36}\,\mathrm{km}$ , ${{\rm{\Lambda }}}_{1.4}={489}_{-110}^{+114}$ , and ${M}_{\max }={2.20}_{-0.19}^{+0.37}\,{M}_{\odot }$ (90% credible levels), where R _1.4 /Λ _1.4 are the radius/tidal deformability of a canonical 1.4 M _⊙ NS, and ${M}_{\max }$ is the maximum mass of a nonrotating NS. The results indicate that the implementation of these VAE techniques can obtain reasonable results, while accelerating calculation by a factor of ∼3–10 or more, compared with the original method.

Keywords

• Neutron stars
• Nonparametric inference