Numerical wave propagation aided by deep learning

We propose a deep learning approach for wave propagation in media with multiscale speed, using second-order linear equation model. use neural networks to enhance the accuracy of given inaccurate coarse solver, which under-resolves class and fields interest. Our involves generating training data by computationally efficient solver another sufficiently accurate applied (described their speed profiles) initial fields. find that trained can approximate nonlinear dependence on as long causality is appropriately sampled data. combine neural-network-enhanced parareal algorithm demonstrate coupled improves stability algorithms enhanced solvers.