Data-driven models are promising tools for predicting ocean conditions and enhancing the details of these predictions. In this study, we applied advanced machine learning methods to model sea surface velocity and height in the Gulf of Mexico. To forecast broad ocean conditions, we used a method called Fourier Neural Operators (FNO), designed to balance computational efficiency with accuracy through a specialized loss function that combines grid and spectral space information. For creating high-resolution details from low-resolution data -- a process called downscaling -- we explored two different neural network architectures and compared their performance against simpler linear interpolation. This combination of forecasting and downscaling methods greatly improves the efficiency of ocean forecast and downscaling compared to numerical simulation with limited input variables. Our results highlight that these data-driven techniques can provide reliable, physics-aware predictions that can be useful for quick, localized analyses and in generating statistical predictions.

While data-driven approaches demonstrate great potential in atmospheric modeling and weather forecasting, ocean modeling poses distinct challenges due to complex bathymetry, land, vertical structure, and flow non-linearity. This study introduces OceanNet, a principled neural operator-based digital twin for ocean circulation. OceanNet uses a Fourier neural operator and predictor-evaluate-corrector integration scheme to mitigate autoregressive error growth and enhance stability over extended time scales. A spectral regularizer counteracts spectral bias at smaller scales. OceanNet is applied to the northwest Atlantic Ocean western boundary current (the Gulf Stream), focusing on the task of seasonal prediction for Loop Current eddies and the Gulf Stream meander. Trained using historical sea surface height (SSH) data, OceanNet demonstrates competitive forecast skill by outperforming SSH predictions by an uncoupled, state-of-the-art dynamical ocean model forecast, reducing computation by 500,000 times. These accomplishments demonstrate the potential of physics-inspired deep neural operators as cost-effective alternatives to high-resolution numerical ocean models.