Deep learning models for scientific spatio-temporal downscaling often minimize reconstruction error while failing to preserve physically meaningful multi-scale structure. For sea surface temperature prediction, this can yield outputs that are numerically plausible yet overly smooth, missing mesoscale variability critical to regional ocean dynamics. Existing methods often focus on pixel-wise objectives or single-context conditioning, which limits their ability to preserve spectral fidelity and generalize across regions. To address this, we propose EddyFlow, a representation learning framework for kilometer-scale sea surface temperature downscaling that balances predictive accuracy, scale-dependent structure, and regional generalization. EddyFlow is trained on the Gulf of St.~Lawrence and evaluated in zero-shot and few-shot settings on the Bay of Fundy and the Gulf of Mexico. EddyFlow demonstrates that physics-informed representation learning reduces zero-shot RMSE by 21%, achieves up to 85.6% skill relative to persistence on unseen domains, and maintains near-ideal spectral fidelity with a PSD ratio of $\approx 1.00$.
Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs). However, long-horizon autoregressive prediction remains challenging: local errors accumulate as spectral inconsistency, phase misalignment, or mean drift. Existing methods mainly improve state representations and operator backbones, while leaving the repeatedly applied latent transition increment weakly structured, allowing spectral errors and unstable channel couplings to accumulate during rollout. To address these issues, we propose a geometry-aware incremental neural operator (GeoIncNO) for stable long-horizon PDE prediction. GeoIncNO predicts latent increments for residual advancement and uses lightweight low-rank projectors to regulate channel coupling within active frequency bands derived from the increment spectral energy distribution. To reduce physical-space reconstruction errors, GeoIncNO further introduces a mean--fluctuation decoupled reconstruction mechanism, where stable mean structures and dynamic fluctuations are fused separately, and phase correction is applied only to the zero-mean fluctuation component. Extensive experiments on six PDE benchmarks, covering 1D, 2D, and 3D dynamical systems, show that GeoIncNO achieves consistently strong prediction accuracy, improved rollout stability, and better spectral fidelity compared with competitive neural-operator baselines.