A Hybrid ML‐PDE Framework for Predicting Breaking Ocean Waves

Abstract Wave breaking plays a central role in ocean dynamics, dissipating wave energy and shaping the evolution of the sea surface. Yet, breaking remains difficult to model: envelope‐based models efficiently capture nonlinear wave evolution and are interpretable but exclude breaking, while high‐fidelity direct numerical simulations resolve breaking dynamics but are too computationally demanding for large domains and long timescales. A recent approach has combined a partial differential equation (PDE) for envelope evolution with a machine learning (ML) component trained on laboratory data for breaking. However, experiments necessitate coarse spatial resolution, leading to a loss of resolution, particularly on phase loss. This restricts the breaking correction to be post hoc and prevents surface elevation reconstruction. Here, we introduce a hybrid framework that integrates a neural network within the complex‐valued PDE and applies corrections at each step during time integration, rather than retrospectively, to model wave breaking. This is enabled by training on high‐resolution Reynolds‐averaged Navier‐Stokes simulations. This hybrid approach enables generalization to unseen wave types, allows surface elevation reconstruction, and outperforms existing methods on both simulated and laboratory data sets. Our framework reconfirms the distinct roles of dissipation and nonlinear spectral energy redistribution in breaking evolution. These advances pave the way toward machine‐learning‐enhanced, phase‐resolving ocean wave prediction.