Employing deep-learning techniques for the conservative-to-primitive recovery in binary neutron star simulations

The detection of GW170817, together with its electromagnetic counterparts, has proven that binary neutron star mergers are of central importance to the field of nuclear astrophysics, e.g., through a better understanding of the formation of elements and novel constraints on the supranuclear dense equation of state governing the matter inside neutron stars. Essential for understanding the binary coalescence are numerical-relativity simulations, which typically come with high computational costs requiring high-performance computing facilities. In this work, we build on recent studies to investigate whether novel techniques, such as neural networks, can be employed in the conversion of conservative variables to primitive hydrodynamical variables, such as pressure and density. In this regard, we perform -- to the best of our knowledge -- the first binary neutron star merger simulations in which such methods are employed. We show that this method results in stable simulations, reaching accuracies similar to traditional methods with an overall comparable computational cost. These simulations serve as a proof of principle that, in the future, deep learning techniques could be used within numerical-relativity simulations. However, further improvements are necessary to offer a computational advantage compared to traditional methods.