Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data

Accurate short-term prediction of phase-resolved water wave conditions is crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modeling assumptions that compromise real-time capability or accuracy of the entire prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modeling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO-based network performs better in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and desired output in Fourier space.