Traditional wave forecasting models, although based on energy conservation equations, are computationally expensive. On the other hand, existing deep learning geophysical fluid models, while computationally efficient, often suffer from issues such as energy dissipation in long-term forecasts. This paper proposes a novel energy-balanced deep learning wave forecasting model called OceanCastNet (OCN). By incorporating wind fields at the current, previous, and future time steps, as well as wave fields at the current and previous time steps as input variables, OCN maintains energy balance within the model. Furthermore, the model employs adaptive Fourier operators as its core components and designs a masked loss function to better handle the impact of land-sea boundaries. A series of experiments on the ERA5 dataset demonstrate that OCN can achieve short-term forecast accuracy comparable to traditional models while exhibiting an understanding of the wave generation process. In comparative experiments under both normal and extreme conditions, OCN consistently outperforms the widely used WaveWatch III model in the industry. Even after long-term forecasting, OCN maintains a stable and energy-rich state. By further constructing a simple meteorological model, OCN-wind, which considers energy balance, this paper confirms the importance of energy constraints for improving the long-term forecast performance of deep learning meteorological models. This finding provides new ideas for future research on deep learning geophysical fluid models.

翻译：传统海浪预报模型虽基于能量守恒方程，但计算成本高昂。另一方面，现有深度学习地球物理流体模型虽计算高效，却常面临长期预报中能量耗散等问题。本文提出了一种新颖的能量平衡深度学习海浪预报模型——OceanCastNet（OCN）。通过将当前、先前及未来时间步的风场，以及当前与先前时间步的浪场作为输入变量，OCN在模型内部保持了能量平衡。此外，该模型采用自适应傅里叶算子作为核心组件，并设计了掩码损失函数以更好地处理陆海边界的影响。基于ERA5数据集的一系列实验表明，OCN能够达到与传统模型相当的短期预报精度，同时展现出对波浪生成过程的理解能力。在常规与极端条件下的对比实验中，OCN始终优于业界广泛使用的WaveWatch III模型。即使经过长期预报，OCN仍能保持稳定且能量充沛的状态。通过进一步构建考虑能量平衡的简易气象模型OCN-wind，本文证实了能量约束对于提升深度学习气象模型长期预报性能的重要性。这一发现为未来深度学习地球物理流体模型的研究提供了新思路。