  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.
