  Recent advances in wave modeling use sufficiently accurate fine solver
outputs to train a neural network that enhances the accuracy of a fast but
inaccurate coarse solver. In this paper we build upon the work of Nguyen and
Tsai (2023) and present a novel unified system that integrates a numerical
solver with a deep learning component into an end-to-end framework. In the
proposed setting, we investigate refinements to the network architecture and
data generation algorithm. A stable and fast solver further allows the use of
Parareal, a parallel-in-time algorithm to correct high-frequency wave
components. Our results show that the cohesive structure improves performance
without sacrificing speed, and demonstrate the importance of temporal dynamics,
as well as Parareal, for accurate wave propagation.
