Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model

In a variety of scientific and engineering domains, the need for high-fidelity and efficient solutions for high-frequency wave propagation holds great significance. Recent advances in wave modeling use sufficiently accurate fine solver outputs to train a neural networks that enhances the accuracy of a fast but inaccurate coarse solver. A stable and fast solver allows the use of Parareal, a parallel-in-time algorithm to correct high-frequency wave components. In this paper we build upon the work of Nguyen and Tsai (2023) and present a unified system that integrates a numerical solver with a neural network into an end-to-end framework. In the proposed setting, we investigate refinements to the deep learning architecture, data generation algorithm and Parareal scheme. 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.