On the Deterministic Prediction of Water Waves

Klein, Marco; Dudek, Matthias; Clauss, Günther F.; Ehlers, Sören; Behrendt, Joachim; Hoffmann, Norbert; Onorato, Miguel

doi:10.3390/fluids5010009

Cited by 36 publications

(32 citation statements)

References 42 publications

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“…Other aggregate measures of fit exist, including the ‘surface similarity parameter’ developed by Perlin & Bustamante (2016) and used to investigate deterministic wave predictions in Klein et al. (2020).…”

Section: Resultsmentioning

confidence: 99%

“…2017; Klein et al. 2020). Because of its lack of bandwidth restrictions, our method is applicable to both narrow JONSWAP spectra (as in § 4.1) as well as broad PM spectra (as in § 4.2).…”

Section: Discussionmentioning

confidence: 99%

“…2018; Klein et al. 2020; Law et al. 2020), engineering design spectra will be used to generate the synthetic sea surfaces herein.…”

Section: Synthetic Sea Surfaces and Measurementsmentioning

confidence: 99%

“…crests in one signal coincide with crests in the second, while −1 means perfect negative correlation, where crests in one signal coincide with troughs in the second. Other aggregate measures of fit exist, including the 'surface similarity parameter' developed by Perlin & Bustamante (2016) and used to investigate deterministic wave predictions in Klein et al (2020). For the three values of in table 1, the correlation ρ between sea and forecast is computed at three forecasting times t = 30, 60 and 90 s throughout the predictable interval bounded by the nonlinear group velocities (see figure 1).…”

Section: Examples Based On Jonswap Spectramentioning

confidence: 99%

“…Klein et al. (2020) have compared several nonlinear Schrödinger models to HOS in a variety of conditions, and found that the inclusion of higher-order dispersion in NLS is crucial in achieving accuracy over a variety of conditions.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic wave forecasting with the Zakharov equation

Stuhlmeier

Stiassnie

2021

J. Fluid Mech.

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Section: Resultsmentioning

confidence: 99%

“…2017; Klein et al. 2020). Because of its lack of bandwidth restrictions, our method is applicable to both narrow JONSWAP spectra (as in § 4.1) as well as broad PM spectra (as in § 4.2).…”

Section: Discussionmentioning

confidence: 99%

“…2018; Klein et al. 2020; Law et al. 2020), engineering design spectra will be used to generate the synthetic sea surfaces herein.…”

Section: Synthetic Sea Surfaces and Measurementsmentioning

confidence: 99%

Section: Examples Based On Jonswap Spectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deterministic wave forecasting with the Zakharov equation

Stuhlmeier

Stiassnie

2021

J. Fluid Mech.

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$$\hbox {U}^p$$-Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

et al. 2023

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In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatio-temporal dynamics. Depending on the required a priori knowledge about the underlying processes, a spectrum of black-box end-to-end learning approaches, physics-informed neural networks, and data-informed discrepancy modeling approaches can be identified. In this work, we propose a purely data-driven approach that uses fully convolutional neural networks to learn spatio-temporal dynamics directly from parameterized datasets of linear spatio-temporal processes. The parameterization allows for data fusion of field quantities, domain shapes, and boundary conditions in the proposed U$$^p$$ p -Net architecture. Multi-domain U$$^p$$ p -Net models, therefore, can generalize to different scenes, initial conditions, domain shapes, and domain sizes without requiring re-training or physical priors. Numerical experiments conducted on a universal and two-dimensional wave equation and the transient heat equation for validation purposes show that the proposed U$$^p$$ p -Net outperforms classical U-Net and conventional encoder–decoder architectures of the same complexity. Owing to the scene parameterization, the U$$^p$$ p -Net models learn to predict refraction and reflections arising from domain inhomogeneities and boundaries. Generalization properties of the model outside the physical training parameter distributions and for unseen domain shapes are analyzed. The deep learning flow map models are employed for long-term predictions in a recursive time-stepping scheme, indicating the potential for data-driven forecasting tasks. This work is accompanied by an open-sourced code.

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