Data-Driven Generation of Neutron Star Equations of State Using Variational Autoencoders

We develop a machine learning model based on a structured variational autoencoder (VAE) framework to reconstruct and generate neutron star (NS) equations of state (EOS). The VAE consists of an encoder network that maps high-dimensional EOS data into a lower-dimensional latent space and a decoder network that reconstructs the full EOS from the latent representation. The latent space includes supervised NS observables derived from the training EOS data, as well as latent random variables corresponding to additional unspecified EOS features learned automatically. Sampling the latent space enables the generation of new, causal, and stable EOS models that satisfy astronomical constraints on the supervised NS observables, while allowing Bayesian inference of the EOS incorporating additional multimessenger data, including gravitational waves from LIGO/Virgo and mass and radius measurements of pulsars. Based on a VAE trained on a Skyrme EOS dataset, we find that a latent space with two supervised NS observables, the maximum mass $(M_{\max})$ and the canonical radius $(R_{1.4})$, together with one latent random variable controlling the EOS near the crust--core transition, can already reconstruct Skyrme EOSs with high fidelity, achieving mean absolute percentage errors of approximately $(0.15\%)$ for $(M_{\max})$ and $(R_{1.4})$ derived from the decoder-reconstructed EOS.