Machine learning approximation for fast and accurate prediction of nonlinear four-wave interactions in spectral wave models

Journal article

Operational wave forecasting requires a delicate balance between the accuracy and computational speed of the spectral wave model used, in which the nonlinear wave–wave interaction ‘source’ term plays an important role. The exact formulation of these non-linear four-wave interactions requires solving the six-dimensional Boltzmann integral, an extremely time-consuming process that has challenged researchers for over half a century. To match the computational speed deemed by practical applications, almost all state-of-the-art operational wave models rely on simplified approximations such as Discrete Interaction Approximation (DIA) with known deficiencies.

In this study, we employ a fully convolutional encoder–decoder architecture for estimating the nonlinear four-wave interaction term. The model is trained on ERA5 reanalysis wave spectra covering a wide range of geographical locations and thus of various sea-states. To evaluate its robustness, the model is first tested on ERA5 data at unseen locations. The results show that the proposed model is capable of predicting WRT nonlinear interaction at a comparable computational speed to DIA. We further assessed the model’s performance on time-evolving wave growth simulations, which show that the proposed model generalizes well beyond its training conditions and shows strong potential for application under more complex wave scenarios. The current formulation is for deep water waves but may be extended to finite depth. This new machine learning based approach not only paves the way for fast and accurate predictions of nonlinear source terms, but also heralds a new machine learning based pipeline for operational wave forecasting.

Authors: Chen, J; Adcock, TAA; Liu, Q; Clark, R; Tang, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Wiley
• Journal: Journal of Geophysical Research: Machine Learning and Computation
• Volume: 3
• Issue: 1
• Article number: e2025JH000864
• Publication date: 2025-12-29
• Acceptance date: 2025-12-18
• DOI: 10.1029/2025jh000864
• EISSN: 2993-5210
• ISSN: 2993-5210
• Language: English
• Keywords: nonlinear wave-wave interactions; machine learning; wave modeling