Deep operator network prediction of velocity profiles in combined wave-current bottom boundary layers

Accurate prediction of the velocity profiles in combined wave-current bottom boundary layers is essential for offshore engineering applications. While our previous work in Yin et al. (2026) proposed data-driven methods to model the spatiotemporally varying velocity profiles, it relied on empirical mathematical expressions for both the wave and current parts. This study introduces an advanced framework that utilizes the Deep Operator Network (DeepONet) architecture to learn the operators mapping the flow parameters to the velocity profiles. A separable architecture is further used to optimize the training efficiency. Unlike traditional models, there is no need for empirical mathematical expressions or predefined profile shapes for this framework, allowing it to capture nonlinear flow features directly from data. Moreover, the DeepONet model provides a continuous spatiotemporal mapping, enabling the simultaneous prediction of velocity as a function of both vertical position and time within the wave cycle. The effectiveness of the proposed model is demonstrated through validation against experimental measurements and through inverse reconstruction of the complete velocity profiles from a single reference current velocity measurement.