Physics-Informed Neural Operators for Spatiotemporal Dissolved Oxygen Forecasting

摘要

Forecasting dissolved oxygen (DO) in coastal waters is important for assessing aquatic habitat conditions and ecosystem health, yet remains challenging due to nonlinear physical--biogeochemical interactions, multiscale environmental forcing, and sparse spatial observations. Existing data-driven approaches often model individual monitoring stations independently, rely on fixed spatial discretizations that limit prediction at unseen locations, or make limited use of known physical structure. We develop a physics-informed neural operator framework for continuous spatiotemporal DO forecasting, which maps multivariate environmental time series together with spatial coordinates directly to DO concentrations. The framework combines a multi-scale causal temporal encoder for capturing environmental forcing across multiple temporal scales with a Fourier-based spatial decoder whose learnable frequencies are initialized through empirical orthogonal function (EOF) structure. A multi-head fusion module further models nonlinear interactions between temporal forcing representations and spatial features beyond the standard bilinear DeepONet formulation. Physical constraints are incorporated into the learning objective to regularize the predicted spatiotemporal field, and we provide a PAC-style analysis characterizing their effect on the model's Rademacher complexity. Experiments across multiple coastal and estuarine datasets demonstrate consistent improvements over representative temporal, spatiotemporal, and operator-learning baselines, including at spatial locations not observed during training. The results further show that the proposed framework maintains stable performance across different regions and observational settings, highlighting the potential of combining continuous operator learning with domain-specific physical structure for data-sparse environmental forecasting.