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We consider strongly-nonlinear and weakly-dispersive surface water wavesgoverned by equations of Boussinesq type, known as the Serre-Green-Naghdisystem; it describes future states of the free water surface and depth averagedhorizontal velocity, given their initial state. The lack of knowledge of thevelocity field as well as the initial states provided by measurements lead toan ill-posed problem that cannot be solved by traditional techniques. To thisend, we employ physics-informed neural networks (PINNs) to generate solutionsto such ill-posed problems using only data of the free surface elevation anddepth of the water. PINNs can readily incorporate the physical laws and theobservational data, thereby enabling inference of the physical quantities ofinterest. In the present study, both experimental and synthetic (generated bynumerical methods) training data are used to train PINNs. Furthermore,multi-fidelity data are used to solve the inverse water wave problem byleveraging both high- and low-fidelity data sets. The applicability of the PINNmethodology for the estimation of the impact of water waves onto solidobstacles is demonstrated after deriving the corresponding equations. Thepresent methodology can be employed to efficiently design offshore structuressuch as oil platforms, wind turbines, etc. by solving the correspondingill-posed inverse water waves problem.

Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations