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<span id="KaiserEtAl2024">L. Kaiser, R. Tsai, and C. Klingenberg, “Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model,” arXiv:2402.02304v4 [math.AP], 2024 [Online]. Available at: <a href="http://arxiv.org/abs/2402.02304v4" target="_blank">http://arxiv.org/abs/2402.02304v4</a></span>
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<pre class="abstract">@unpublished{KaiserEtAl2024,
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author = {Kaiser, Luis and Tsai, Richard and Klingenberg, Christian},
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howpublished = {arXiv:2402.02304v4 [math.AP]},
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title = {Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model},
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url = {http://arxiv.org/abs/2402.02304v4},
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year = {2024}
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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.
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<span id="KwokEtAl2024">F. Kwok and D. N. Tognon, “A parallel in time algorithm based ParaExp for optimal control problems,” arXiv:2406.11478v1 [cs.DC], 2024 [Online]. Available at: <a href="http://arxiv.org/abs/2406.11478v1" target="_blank">http://arxiv.org/abs/2406.11478v1</a></span>
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author = {Kwok, Felix and Tognon, Djahou N},
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howpublished = {arXiv:2406.11478v1 [cs.DC]},
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title = {A parallel in time algorithm based ParaExp for optimal control problems},
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url = {http://arxiv.org/abs/2406.11478v1},
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year = {2024}
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}
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We propose a new parallel-in-time algorithm for solving optimal control problems constrained bypartial differential equations. Our approach, which is based on a deeper understanding of ParaExp,considers an overlapping time-domain decomposition in which we combine the solution of homogeneous problems using exponential propagation with the local solutions of inhomogeneous problems.The algorithm yields a linear system whose matrix-vector product can be fully performed in parallel.We then propose a preconditioner to speed up the convergence of GMRES in the special cases ofthe heat and wave equations. Numerical experiments are provided to illustrate the efficiency of ourpreconditioners.
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<span id="LeeEtAl2022b">C.-O. Lee, Y. Lee, and J. Park, “A Parareal Architecture for Very Deep Convolutional Neural Networks,” in <i>Lecture Notes in Computational Science and Engineering</i>, Springer International Publishing, 2022, pp. 407–415 [Online]. Available at: <a href="http://dx.doi.org/10.1007/978-3-030-95025-5_43" target="_blank">http://dx.doi.org/10.1007/978-3-030-95025-5_43</a></span>
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author = {Lee, Chang-Ock and Lee, Youngkyu and Park, Jongho},
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booktitle = {Lecture Notes in Computational Science and Engineering},
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doi = {10.1007/978-3-030-95025-5_43},
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isbn = {9783030950255},
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issn = {2197-7100},
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pages = {407–415},
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publisher = {Springer International Publishing},
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title = {A Parareal Architecture for Very Deep Convolutional Neural Networks},
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url = {http://dx.doi.org/10.1007/978-3-030-95025-5_43},
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year = {2022}
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