Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909789332701184 |
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| author | Kaiser, Luis Tsai, Richard Klingenberg, Christian |
| author_facet | Kaiser, Luis Tsai, Richard Klingenberg, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model Kaiser, Luis Tsai, Richard Klingenberg, Christian Analysis of PDEs Machine Learning 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. |
| title | Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model |
| topic | Analysis of PDEs Machine Learning |
| url | https://arxiv.org/abs/2402.02304 |