A deep operator network method for high-precision and robust real-time ocean wave prediction

Real-time wave prediction is crucial for optimizing offshore renewable energy capture and ensuring the safety of floating offshore structures. However, the stochastic and nonlinear nature of waves presents significant challenges for accurate and robust predictions. This study proposes a wave prediction model based on the Deep Operator Network (DON-WP), which learns a nonlinear operator to map historical wave heights to future wave heights. By leveraging this operator-learning framework, the model demonstrates strong generalization across the function space, enabling it to adapt to previously unseen wave conditions. Specifically, the branch net encodes historical wave data into functional representations, while the trunk net captures prediction targets as evaluation points of the output function. These outputs are then combined through element-wise operations to generate precise wave predictions. The model's generalization ability and robustness are validated using wave tank experimental data across multiple sea states, and its performance is compared with the Long Short-Term Memory network-based probabilistic prediction model (Deep-WP). Results show that DON-WP, trained on a single sea state, achieves over 30% higher accuracy across most prediction horizons and up to a 60% improvement for shorter prediction steps compared to Deep-WP, which requires retraining for each sea state. This study highlights DON-WP as an effective approach for wave dynamics modeling, with significant potential to advance offshore renewable energy systems and enhance the safety of offshore structures.