Beyond the Courant-Friedrichs-Lewy condition: Numerical methods for the wave problem using deep learning

We investigate a numerical method for approximating the solution of the one dimensional acoustic wave problem, when violating the numerical stability condition. We use deep learning to create an explicit non-linear scheme that remains stable for larger time steps and produces better accuracy than the reference implicit method. The proposed spatio-temporal neural-network architecture is additionally enhanced during training with a physically-informed term, adapting it to the physical problem it is approximating and thus more accurate.