Towards accelerated nuclear-physics parameter estimation from binary neutron star mergers: Emulators for the Tolman-Oppenheimer-Volkoff equations

TL;DR

This paper develops and compares machine learning emulators for solving the TOV equations, enabling faster Bayesian inference of neutron star properties from gravitational-wave data.

Contribution

It introduces MLP, GP, and RBM emulators for TOV equations, demonstrating improved speed and accuracy for nuclear-physics parameter estimation in neutron star mergers.

Findings

MLP emulators outperform GP and RBM in accuracy.

RBM provides the fastest speedup over full TOV solver.

Emulators produce posterior distributions consistent with full solutions.

Abstract

Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman-Oppenheimer-Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: Multilayer Perceptrons (MLP), Gaussian Processes (GP), and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms whereas the RBM results in the largest speedup with respect to the full, high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation, and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.