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

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 free depth averaged horizontal velocity, given their initial state. The lack knowledge velocity field well provided measurements lead to an ill-posed problem that cannot be solved traditional techniques. To this end, we employ physics-informed neural networks (PINNs) generate solutions such problems using only data elevation water. PINNs can readily incorporate physical laws observational data, thereby enabling inference quantities interest. In present study, both experimental synthetic (generated numerical methods) training are used train PINNs. Furthermore, multi-fidelity solve inverse wave leveraging high- low-fidelity sets. applicability PINN methodology for estimation impact onto solid obstacles is demonstrated after deriving corresponding equations. employed efficiently design offshore structures oil platforms, wind turbines, etc. solving problem.