Physics-Informed Residual Learning for Directional Wave Spectrum Reconstruction

Abstract

This study investigates the problem of reconstructing the two-dimensional ocean wave spectrum using sparse input data using a Physics-informed Surrogate model equipped with residual learning. Analytical models such as the Fourier-based expansion, NDBC approximation, and the Maximum Entropy Method (MEM) provide a physically grounded solution but are limited either in flexibility or are computationally expensive. Pure machine learning models offer great flexibility but lack the physical consistency needed to handle diverse wave climates.

To overcome these limitations, this study proposes a hybrid approach that combines the analytical baseline reconstruction with physics-informed data-driven residual learning. The baseline analytical reconstruction is constructed using the Fourier expansion from the one-dimensional spectrum and directional moments. The neural network is trained to learn the residual corrections of this baseline's outputs. Additional physics-informed constraints are incorporated to enforce energy conservation and directional moments consistency to better guide the model during the training process.

The experiments conducted on the ERA5 reanalysis datasets show that the hybrid combination of physics-informed data- driven models with residual learning techniques performed significantly better, improving the reconstruction accuracy compared to pure machine learning models. The proposed model outperformed standard machine learning approaches, even those that were equipped with residual learning without physics loss constraints, achieving substantial reductions in reconstruction error. However, analytical methods like MEM and NDBC remain the most accurate overall in diverse sea conditions. Generalization experiments on unseen North Sea data show that machine learning models are sensitive to domain shift, whereas analytical methods demonstrate great robustness.