Nonparametric Representation of Neutron Star Equation of State Using Variational Autoencoder

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 \citet{2021ApJ...919...11H} as the training set and try different settings of the neural network, then we get an EoS generator (trained VAE's decoder) with four parameters. We use the mass\textendash{}tidal-deformability data of binary neutron star (BNS) merger event GW170817, the mass\textendash{}radius data of PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, and 4U 1702-429, and the nuclear constraints to perform the joint Bayesian inference. The overall results of the analysis that includes all the observations are $R_{1.4}=12.59^{+0.36}_{-0.42}\,\rm km$, $\Lambda_{1.4}=489^{+114}_{-110}$, and $M_{\rm max}=2.20^{+0.37}_{-0.19}\,\rm M_\odot$ ($90\%$ credible levels), where $R_{1.4}$/$\Lambda_{1.4}$ are the radius/tidal-deformability of a canonical $1.4\,\rm M_\odot$ NS, and $M_{\rm max}$ is the maximum mass of a non-rotating NS. The results indicate that the implementation of the VAE techniques can obtain the reasonable results, while accelerate calculation by a factor of $\sim$ 3\textendash10 or more, compared with the original method.