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

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.

Efficient Numerical Wave Propagation Enhanced by an End-to-End Deep Learning Model

In a variety of scientific and engineering domains, ranging from seismic modeling to medical imaging, 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 neural networks that enhance the accuracy of a fast but inaccurate coarse solver. A stable and fast solver further allows the use of Parareal, a parallel-in-time algorithm to retrieve and correct high-frequency wave components. 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 deep learning components into an end-to-end framework. In the proposed setting, we investigate refinements to the neural network architecture, data generation algorithm and Parareal scheme. Our results show that the cohesive structure significantly improves performance without sacrificing speed, and demonstrate the importance of temporal dynamics, as well as Parareal iterations, for accurate wave propagation.