Fourier Neural Operators for Emulating Ocean Models: Towards a Knowledge-Driven Machine Learning

Accurate forecasting of ocean dynamics is essential for understanding the distribution of heat, salinity, and nutrients in the ocean. While data-driven machine learning models offer promising solutions for ocean forecasting and emulating ocean models, they often lack physical consistency (i.e., adherence to the physical laws of fluid dynamics) and explainability. In this study, we introduce a deep neural network architecture leveraging Fourier Neural Operators (FNO) for efficient forecasting of ocean surface dynamics: sea level, temperature, and salinity. FNOs excel in learning resolution-invariant solutions of partial differential equations (PDEs), offering a scalable alternative to traditional physics-based models. Operating in Fourier space enables differentiation to be treated as multiplication, which is the basis of spectral methods used for solving PDEs, including the Navier-Stokes equations that govern hydrodynamic models. Therefore, it is intuitive that by directly parameterizing the integral kernel in Fourier space, the model can learn PDE solutions more efficiently. FNOs also enable training on low-resolution data and evaluation on high-resolution data, which helps minimize the growth of autoregressive errors.

Our model is trained on the Baltic Sea Physics Analysis and Forecast dataset to predict sea surface parameters, including sea level, temperature, and salinity. The Baltic Sea is a non-tidal, semi-enclosed sea with a complex coastline, shallow sea, significant salinity gradients, and permanent stratification, which makes it a unique and challenging testbed for ocean modelling. Input variables include the initial state, atmospheric forcing, and bathymetry, and the model is trained to predict ocean surface dynamics (sea level, temperature, and salinity) and learn the mapping from time t to t+1. In the inference step, the model is initialized with the initial sea surface inputs from an out-of-sample testing dataset and iteratively generates forecasts for τ time steps. Evaluation of the model demonstrates competitive forecasting skill compared to physical models, while significantly reducing computational costs. This study highlights the potential of FNOs to advance knowledge-driven machine learning models for ocean forecasting. These models, as cost-effective alternatives to high-resolution physical ocean models, can pave the way for more efficient, scalable approaches to understanding and predicting ocean dynamics.