Numerical methods are powerful tools for advancing our understanding of quantum gravity. In this talk, I will introduce two complementary numerical approaches. The first focuses on solving nonlinear partial differential equations that arise in Loop Quantum Gravity (LQG)-inspired effective models. This framework enables us to investigate the formation and evolution of shock waves in spherically symmetric gravitational collapse. The second approach involves the use of complex critical points, Lefschetz thimble techniques, and the Metropolis Monte Carlo algorithm to study the Lorentzian path integral in Spinfoam models and Quantum Regge Calculus. These methods offer new insights into quantum cosmology and black-to-white hole transitions.
Laurent Freidel, Joshua Kirklin