Nonparametric model for the equations of state of neutron star from deep neural network

TL;DR

This paper introduces a deep neural network-based nonparametric framework to model the neutron star equation of state, effectively incorporating uncertainties and fitting observational data to derive key neutron star properties.

Contribution

It develops a novel nonparametric approach using neural networks and Gaussian processes to estimate the neutron star EOS, accounting for systematic uncertainties and observational constraints.

Findings

Maximum neutron star mass estimated at ~2.4 solar masses.

Neutron star radius at 1.4 solar masses is about 12.3 km.

Results align with previous studies, validating the method.

Abstract

It is of great interest to understand the equation of state (EOS) of the neutron star (NS), whose core includes highly dense matter. However, there are large uncertainties in the theoretical predictions for the EOS of NS. It is useful to develop a new framework, which is flexible enough to consider the systematic error in theoretical predictions and to use them as a best guess at the same time. We employ a deep neural network to perform a non-parametric fit of the EOS of NS using currently available data. In this framework, the Gaussian process is applied to represent the EOSs and the training set data required to close physical solutions. Our model is constructed under the assumption that the true EOS of NS is a perturbation of the relativistic mean-field model prediction. We fit the EOSs of NS using two different example datasets, which can satisfy the latest constraints from the massive neutron stars, NICER, and the gravitational wave of the binary neutron stars. Given our assumptions, we find that a maximum neutron star mass is $2.38^{+0.15}_{-0.13} M_\odot$ or $2.41^{+0.15}_{-0.14}$ at $95\%$ confidence level from two different example datasets. It implies that the $1.4 M_\odot$ radius is $12.31^{+0.29}_{-0.31}$ km or $12.30^{+0.35}_{-0.37}$ km. These results are consistent with results from previous studies using similar priors. It has demonstrated the recovery of the EOS of NS using a nonparametric model.