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

Abstract: We emulate the Tolman-Oppenheimer-Volkoff (TOV) equations, including tidal deformability, for neutron stars using a novel hybrid method based upon the Dynamic Mode Decomposition (DMD) for the first time. This new 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 phenomenological equations of state (EOS) with fixed parameters and with a freely-varying parametric Quarkyonic EOS. Our results produce a significant computational speed-up of $\approx 3 \times 10^4$ compared to high fidelity (HF) calculations using standard Runge-Kutta methods, providing an efficient emulator for the numerous TOV evaluations required by multi-messenger astrophysical frameworks that infer constraints on the EOS from neutron star mergers. 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 developed in this work will be openly available in a public GitHub repository for community modification and use.