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

2024-02-04

arXiv.org

AI Summary

This work addresses the longstanding challenge of simultaneously achieving high fidelity and computational efficiency in high-frequency wave propagation simulation. Methodologically, we propose an end-to-end framework that deeply integrates numerical solvers with deep learning: (1) a unified architecture jointly optimizes a coarse-grid PDE solver and a convolutional neural network; (2) enhanced network design and physics-informed data generation improve generalization and physical consistency; (3) Parareal—a time-parallel algorithm—is, for the first time, embedded into the deep learning pipeline to enable iterative correction of high-frequency components. Experiments demonstrate that the framework improves coarse-grid solution accuracy by one to two orders of magnitude while maintaining near-real-time inference speed. The core contribution is a differentiable, scalable “numerical + learning + parallel” co-modeling paradigm. We rigorously validate that temporal dynamic modeling combined with Parareal-based correction delivers critical accuracy gains for high-frequency wave propagation.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• Enhances accuracy of fast but inaccurate wave solvers
• Integrates numerical solver with deep learning
• Improves performance without sacrificing computational speed

Innovation

• End-to-end deep learning enhances wave propagation.
• Integrated numerical solver with neural network.
• Parareal algorithm corrects high-frequency waves.