Gravitational-wave model for neutron star merger remnants with supervised learning

We present a time-domain model for the gravitational waves emitted by equal-mass binary neutron star merger remnants for a fixed equation of state. We construct a large set of numerical relativity simulations for a single equation of state consistent with current constraints, totaling 157 equal-mass binary neutron star merger configurations. The gravitational-wave model is constructed using the supervised learning method of K-nearest neighbor regression. As a first step toward developing a general model with supervised learning methods that accounts for the dependencies on equation of state and the binary masses of the system, we explore the impact of the size of the dataset on the model. We assess the accuracy of the model for a varied dataset size and number density in total binary mass. Specifically, we consider five training sets of simulations uniformly distributed in total binary mass. We evaluate the resulting models in terms of faithfulness using a test set of 30 additional simulations that are not used during training and which are equidistantly spaced in total binary mass. The models achieve faithfulness with maximum values in the range of 0.980 to 0.995. We assess our models simulating signals observed by the three-detector network of Advanced LIGO-Virgo. We find that all models with training sets of size equal to or larger than 40 achieve an unbiased measurement of the main gravitational-wave frequency. We confirm that our results do not depend qualitatively on the choice of the (fixed) equation of state. We conclude that training sets, with a minimum size of 40 simulations, or a number density of approximately 11 simulations per 0.1⁢𝑀⊙ of total binary mass, suffice for the construction of faithful templates for the postmerger signal for a single equation of state and equal-mass binaries, and lead to mean faithfulness values of ℱ ≃0.95. Our model being based on only one fixed equation of state represents only a first step toward a method that is fully applicable for gravitational-wave parameter estimation. However, our findings are encouraging since we show that our supervised learning model built on a set of simulations for a fixed equation of state successfully recovers the main gravitational-wave features of a simulated signal obtained using another equation of state. This may indicate that the extension of this model to an arbitrary equation of state may actually be achieved with a manageable set of simulations.