Star Log-extended eMulation: a method for efficient computation of the Tolman-Oppenheimer-Volkoff equations

TL;DR

This paper introduces the Star Log-extended eMulation (SLM), a novel method based on Dynamic Mode Decomposition for efficiently emulating the TOV equations, significantly speeding up neutron star modeling and enabling advanced EOS analysis.

Contribution

The paper presents SLM, a new DMD-based emulation technique that accurately reproduces TOV solutions with high speed, facilitating rapid EOS parameter studies and uncertainty quantification.

Findings

Achieves a speed-up of approximately 24,000 times for fixed EOS predictions.

Attains a speed-up of approximately 70,000 times for two-parameter EOS evaluations.

Successfully emulates TOV solutions for various EOSs with high fidelity.

Abstract

We emulate the Tolman-Oppenheimer-Volkoff (TOV) equations, including tidal deformability, for neutron stars using a new method based upon the Dynamic Mode Decomposition (DMD). This method, which we call Star Log-extended eMulation (SLM), utilizes the underlying logarithmic behavior of the differential equations to enable accurate emulation of the nonlinear system. We show predictions for well-known equations of state (EOSs) with fixed parameters using the SLM, accurately recreating high-fidelity results while achieving a computational speed-up of $\approx 2.4 \times 10^4$. We test our parametric SLM method for a two-parameter quarkyonic EOS against high-fidelity RK4 TOV calculations and find a computational speedup of $\approx 7.0 \times 10^4$. Hence, SLM is an efficient emulator for the numerous TOV evaluations required by multi-messenger astrophysical frameworks that infer constraints on the EOS. The ability of the SLM algorithm to learn a mapping between parameters of the EOS and subsequent neutron star properties also opens up potential extensions for assisting in computationally prohibitive uncertainty quantification (UQ) for any type of EOS. The source code for the methods employed in this work is openly available in a public GitHub repository for community modification and use.