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 $\{ 20,40, 60, 80, 100\}$ 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 $0.1\,M_\odot$ of total binary mass, suffice for the construction of faithful templates for the post-merger signal for a single equation of state and equal-mass binaries (abbreviated).