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

arXiv: https://arxiv.org/abs/2402.02304 · HTML: https://mlsanity.com/paper/2402.02304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 6 of 6)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [The One Hundred Layers Tiramisu: Fully Convolutional DenseNets for Semantic Segmentation](https://mlsanity.com/paper/1611.09326/) (2016)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [U-Net Transformer: Self and Cross Attention for Medical Image Segmentation](https://mlsanity.com/paper/2103.06104/) (2021)
- [Parareal with a physics-informed neural network as coarse propagator](https://mlsanity.com/paper/2303.03848/) (2023)

## Abstract (arXiv)

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 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.