EddyCast: Physics-as-Bypass for 3D Mesoscale Eddy Forecasting

Existing physics-informed ocean forecasting often incorporates physical knowledge through loss penalties or prescribed physical structures, which can limit the flexible integration of physical priors with data-driven representations. We propose Physics-as-Bypass, a physical-embedding paradigm for medium-range 3D mesoscale eddy forecasting. Its zero-initialized residual bypass preserves the data-driven baseline at initialization while enabling adaptive integration of physical priors through a learnable pointwise projection. Based on this paradigm, EddyCast uses fixed analytical operators to provide physically grounded guidance, while EddyCast-VMoD employs learnable vertical modal decomposition to quantify prior-data alignment and modal saturation. We further introduce EddyCast-Prob, which equips the shared backbone with an EDM head for probabilistic ensemble forecasting. Experiments show that EddyCast consistently outperforms strong deterministic baselines. Modal ablations and subspace analysis reveal a strong low-rank vertical structure in 3D eddy temperature-salinity fields and show that optimization moves learned representations toward data-aligned physical subspaces. We further explain modal saturation through residual-energy coverage and basis alignment, showing that forecasting-optimal physical dimensionality need not coincide with the effective rank of the data.