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

TL;DR

This paper develops a physics-informed neural network approach using multi-fidelity data to solve ill-posed inverse water wave problems governed by Serre-Green-Naghdi equations, with applications to offshore structure design.

Contribution

It introduces a multi-fidelity PINN framework for inverse water wave problems, effectively integrating experimental and synthetic data to infer physical quantities.

Findings

PINNs successfully estimate water surface and velocity fields from limited data.

Multi-fidelity data improve the accuracy and robustness of the inverse solutions.

Method demonstrates potential for designing offshore structures against water wave impacts.

Abstract

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 (PINNs) to generate solutions to such ill-posed problems using only data of the free surface elevation and depth of the water. PINNs can readily incorporate the physical laws and the observational data, thereby enabling inference of the physical quantities of interest. In the present study, both experimental and synthetic (generated by numerical methods) training data are used to train PINNs. Furthermore, multi-fidelity data are used to solve the inverse water wave problem by leveraging both high- and low-fidelity data sets. The applicability of the PINN methodology for the estimation of the impact of water waves onto solid obstacles is demonstrated after deriving the corresponding equations. The present methodology can be employed to efficiently design offshore structures such as oil platforms, wind turbines, etc. by solving the corresponding ill-posed inverse water waves problem.