Improving the I-Love-Q Universal Relations with Machine Learning

Gravitational wave observations of neutron star mergers play a pivotal role in advancing our understanding of the dense matter equation of state (EOS) and constraining neutron star structures. While gravitational wave (GW) observations from binary neutron star mergers do not precisely constrain the individual tidal deformabilities of the two neutron stars, more stringent bounds can be obtained using EOS insensitive relations, or universal relations, with GW-inferred parameters. However, the universal relations are empirical derivations, with certain degrees of error. These errors are too large for precision measurements accomplished with next generation gravitational wave detectors and are found to induce systematic errors in the inference of the neutron star EOS. Machine learning algorithms offer a promising approach to enhancing the precision of the universal relations by providing a more comprehensive and elaborate analysis of EOS data. We apply PySR, an open-source high-performance symbolic regression library which creates and trains a model to fit to a dataset using given variables, to improve the compactness and tidal Love number relation, and the relation between the symmetric and asymmetric combinations of Love number. We find errors smaller by a factor of 2-3 for the compactness and tidal Love number relation, and a substantially simpler equation for the relation between the symmetric and asymmetric combinations of Love number.