Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time

TL;DR

This paper introduces a physics-informed neural operator framework that reconstructs nonlinear ocean wave fields in real-time from sparse measurements without requiring large labeled datasets, leveraging physical boundary conditions for improved accuracy.

Contribution

The novel PINO framework integrates physical boundary conditions into neural operators, enabling real-time, data-efficient reconstruction of ocean wave fields from sparse data without ground truth during training.

Findings

Accurately reconstructs wave fields from sparse measurements

Generalizes well across diverse wave conditions

Operates in real-time for practical applications

Abstract

Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or indirect wave measurements. While recent advances in supervised deep learning have shown potential for this purpose, they require large labelled datasets of ground truth wave data, which are infeasible to obtain in real-world scenarios. To overcome this limitation, we propose a Physics-Informed Neural Operator (PINO) framework for reconstructing spatially and temporally phase-resolved, nonlinear ocean wave fields from sparse measurements, without the need for ground truth data during training. This is achieved by embedding residuals of the free surface boundary conditions of ocean gravity waves into the loss function of the PINO, constraining the solution space in a soft manner. After training, we validate our approach using highly realistic synthetic wave data and demonstrate the accurate reconstruction of nonlinear wave fields from both buoy time series and radar snapshots. Our results indicate that PINOs enable accurate, real-time reconstruction and generalize robustly across a wide range of wave conditions, thereby paving the way for operational, data-driven wave reconstruction and prediction in realistic marine environments.