Super-Resolution without High-Resolution label for Black Hole Simulations

The generation of high-resolution simulations is essential for advancing our understanding of the universe's most violent events, such as Black Hole mergers. However, generating Black Hole simulations is limited by prohibitive computational costs and scalability issues, reducing the simulation's fidelity and resolution achievable within reasonable time frames and resources. In this work, we introduce a novel method that circumvents these limitations by applying super-resolution techniques without directly needing high-resolution labels by leveraging the Hamiltonian and momentum constraints -- fundamental equations in general relativity that govern the dynamics of spacetime. Our novel approach addresses the computational inefficiencies of current methods while maintaining the physical accuracy required in numerical relativity simulations. We show that our method creates a two-orders-of-magnitude reduction in numerical error and generalizes to out-of-distribution simulations.