E2E-FANet: A Highly Generalizable Framework for Waves prediction Behind Floating Breakwaters via Exogenous-to-Endogenous Variable Attention

Accurate prediction of waves behind floating breakwaters (FB) is crucial for optimizing coastal engineering structures, enhancing safety, and improving design efficiency. Existing methods demonstrate limitations in capturing nonlinear interactions between waves and structures, while exhibiting insufficient capability in modeling the complex frequency-domain relationships among elevations of different wave gauges. To address these challenges, this study introduces the Exogenous-to-Endogenous Frequency-Aware Network (E2E-FANet), a novel end-to-end neural network designed to model relationships between waves and structures. The E2E-FANetarchitecture incorporates a Dual-Basis Frequency Mapping (DBFM) module that leverages orthogonal cosine and sine bases to extract wave features from the frequency domain while preserving temporal information. Additionally, we introduce the Exogenous-to-Endogenous Cross-Attention (E2ECA) module, which employs cross attention to model the interactions between endogenous and exogenous variables. We incorporate a Temporal-wise Attention (TA) mechanism that adaptively captures complex dependencies in endogenous variables. These integrated modules function synergistically, enabling E2E-FANet to achieve both comprehensive feature perception in the time-frequency domain and precise modeling of wave-structure interactions. To comprehensively evaluate the performance of E2E-FANet, we constructed a multi-level validation framework comprising three distinct testing scenarios: internal validation under identical wave conditions, generalization testing across different wave conditions, and adaptability testing with varying relative water density (RW) conditions. These comprehensive tests demonstrate that E2E-FANet provides accurate waves behind FB predictions while successfully generalizing diverse wave conditions.