Accurate short-term predictions of phase-resolved water wave conditions are 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 modelling assumptions that compromise the real-time capability or accuracy of the subsequent 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 modelling 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 demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

翻译：精确的相位分辨水波条件短期预测对海洋工程决策至关重要。然而，基于遥感的波浪预测模型的初始化首先需要从雷达等稀疏测量数据中重构波面。现有重构方法要么依赖计算密集的优化过程，要么采用过于简化的建模假设，从而影响后续预测过程的实时性或精度。为此，我们提出了一种基于U-Net和傅里叶神经算子(FNO)架构的神经网络相位分辨波面重构新方法。本方法利用均匀一维网格上的合成但高度逼真的训练数据——该数据通过高阶谱方法进行波浪模拟，并结合几何雷达建模方法生成。研究表明，当在每次输入中包含多帧历史雷达快照的时空雷达数据训练时，两种模型均能提供精确的波浪重构结果，并展现出对不同海况的良好泛化能力。值得注意的是，由于FNO在傅里叶空间中采用全局方法学习输入与输出之间的映射关系，其在处理波浪物理强加的数据结构方面表现出更优越的性能。