PhysiOcean: A Spatio-Temporal Operator with Physics-Guided Learning for Coastal Dissolved Oxygen Forecasting

Forecasting dissolved oxygen (DO) across monitoring locations and depth layers is challenging because coastal DO dynamics involve multiscale environmental forcing, strong spatial heterogeneity, and sparse observations. Existing data-driven approaches typically model individual stations independently or rely on fixed spatial decompositions, limiting their ability to jointly represent temporal dynamics and continuous spatial variation. We introduce $\mathbf{PhysiOcean}$, a spatio-temporal operator that maps historical environmental forcing and spatial coordinates to DO concentrations. PhysiOcean combines a multi-scale causal temporal encoder, a learnable Fourier spatial decoder, and a multi-head nonlinear fusion mechanism to learn regional DO fields end-to-end. EOF-guided initialization and physics-guided regularization further incorporate dominant spatial structure and domain knowledge during training. We analyze the expressivity of the proposed fusion mechanism and the complexity of an idealized physics-constrained hypothesis class. Experiments on a 32-year monitoring record from a large, environmentally heterogeneous estuary containing 40 monitoring stations and 800 station-depth locations show that PhysiOcean outperforms sequence, decomposition-based, and operator-learning baselines. Component analyses demonstrate that the temporal encoder, continuous spatial representation, fusion mechanism, EOF initialization, and physics-guided losses provide complementary improvements. PhysiOcean also maintains stronger performance at monitoring locations and depth layers excluded from training, demonstrating within-estuary generalization to unobserved spatial coordinates. Our code is available at https://anonymous.4open.science/r/physiocean/.