Multiscale coupling algorithms using parareal style structures
We are developing a data-driven parallel-in-time iterative method to solve the homogeneous second-order wave equation. The new method involves a coarse-scale propagator and a fine-scale propagator which fully resolves the medium using finer spatial grid and shorter time steps. The fine-scale propagator is run in parallel for short time subintervals. The two propagators are coupled in an iterative way similar to the standard parareal method. We train a Neural Network, which structure mimics the physics of wave propagation, to enhance the accuracy of the coarse-scale propagator such that the parareal iteration stabilizes and hence converges.