Neural networks reconstruction of the dense-matter equation of state from neutron-star parameters

TL;DR

This paper demonstrates that neural networks guided by autoencoder architecture can accurately reconstruct the neutron star equation of state from observable parameters like mass, radius, and tidal deformability, even with limited data.

Contribution

It introduces a neural network approach for precise neutron star equation of state reconstruction using observable parameters, including a study on the impact of observational uncertainties and realistic models.

Findings

Neural networks can generalize the EOS mapping with limited data.

Reconstruction accuracy depends on the number of observations and measurement uncertainties.

The method successfully applies to realistic equations of state.

Abstract

Aims: The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precise reconstruction of the neutron star equation of state, using their observable parameters: masses, radii and tidal deformabilities. In addition we study how well the neutron star radius can be reconstructed using the gravitational-wave only observations of tidal deformability, i.e. quantities which are not related in a straightforward way. Methods: Application of artificial neural network in the equation of state reconstruction exploits the non-linear potential of this machine learning model. Since each neuron in the network is basically a non-linear function, it is possible to create a complex mapping between the input sets of observations and the output equation of state table. Within the supervised training paradigm, we construct a few hidden layer deep neural network on a generated data set, consisting of a realistic equation of state for the neutron star crust connected with a piecewise relativistic polytropes dense core, with parameters representative to the state-of-the art realistic equations of state. Results: We demonstrate the performance of our machine learning implementation with respect to the simulated cases with varying number of observations and measurement uncertainties. Furthermore we study the impact of the neutron star mass distributions on the results. Finally, we test the reconstruction of the equation of state trained on parametric polytropic training set using the simulated mass--radius and mass--tidal-deformability sequences based on realistic equations of state. Neural networks trained with a limited data set are able to generalize the mapping between global parameters and equation of state input tables for realistic models.