2022
DOI: 10.48550/arxiv.2202.02899
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Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations

Abstract: A. We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre-Green-Naghdi system; it describes future states of the free water surface and depth averaged horizontal velocity, given their initial state. The lack of knowledge of the velocity field as well as the initial states provided by measurements lead to an ill-posed problem that cannot be solved by traditional techniques. To this end, we employ physics-informed neural networks (PIN… Show more

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Cited by 2 publications
(1 citation statement)
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“…In recent years physics-informed neural networks (PINNs) [1] emerged as an alternative simple method to solve many problems in computational science and engineering, see, for example [2,3,4,5,6,7,8,9,10,4,11,12,13,14,15]. In particular, PINNs do not require meshes and can efficiently solve forward problems and even ill-posed inverse problems, which are otherwise difficult or sometimes even impossible to solve using traditional numerical methods.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years physics-informed neural networks (PINNs) [1] emerged as an alternative simple method to solve many problems in computational science and engineering, see, for example [2,3,4,5,6,7,8,9,10,4,11,12,13,14,15]. In particular, PINNs do not require meshes and can efficiently solve forward problems and even ill-posed inverse problems, which are otherwise difficult or sometimes even impossible to solve using traditional numerical methods.…”
Section: Introductionmentioning
confidence: 99%