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

TL;DR

This work addresses the uncertainty of neutron star equation of state at intermediate-to-high densities by introducing a structured variational autoencoder that learns a compact latent representation mapping to physically admissible EOSs and NS observables. The model is trained on Skyrme-based EOS data and uses two supervised latent observables, $M_{\max}$ and $R_{1.4}$, plus a single latent variable $z_0$ to accurately reconstruct EOS segments and generate mass-radius relations via the TOV equations. It demonstrates high-fidelity reconstruction (MAPE ~$0.15\%$ for $M_{\max}$ and $R_{1.4}$) and smooth, interpretable EOS variations, including the ability to reproduce the SLy4 EOS when conditioned on its observables. This framework enables efficient, Bayesian-ready exploration of EOS uncertainty under multimessenger constraints, with potential to integrate multiple nuclear models and phase-transition scenarios.

Abstract

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.

Figures (7)

• Figure 1: The Variational Autoencoder Framework.
• Figure 2: Pairwise distributions for the supervised and latent variables for the test dataset. The selected values of $M_{\max}$ and $R_{1.4}$, along with the intervals used to probe latent space sensitivity in the reconstructed EOS, are indicated by the dashed lines. For the latent variable $z_0$, a standard normal distribution (orange) is overlaid on the histogram.
• Figure 3: Decoder MAPE comparison for both supervised latent observables defined in Fig. \ref{['fig:VAE']}. The MAPE is computed for each combination of latent dimensionality, $\kappa$, and $\eta$ used during training. The hyperparameter and dimensionality combo selected for further analysis is outlined with a red box.
• Figure 4: EOS $P(n_B)$ (left panel) generated by varying the supervised latent parameter $M_{\max}$ about a central value of $2.1\,M_\odot$, while holding $R_{1.4}$ and $z_0$ fixed. For each chosen $M_{\max}$, the corresponding EOS is decoded from the VAE latent space and evaluated over a common pressure grid. For comparison, we also show the SLy4 EOS (dashed). The right panel shows the mass--radius curves computed from each corresponding EOS.
• Figure 5: Same as Fig. \ref{['fig:EOS_sensitivity_Mmax_P_vs_nB']}, except the supervised latent parameter $M_{\max}$ and the latent variable $z_0$ are held fixed while varying $R_{1.4}$ about a central value of $12.5\,\mathrm{km}$.