Non-Temporal Environmental Factor-Driven Dissolved Oxygen Prediction via Physics-Informed Regression for Sustainable Environmental Monitoring

Dissolved oxygen (DO) is a critical indicator for assessing marine ecological health and hypoxia risk. Most existing DO prediction studies rely on time-series forecasting models, which require continuous temporal observations and are often unreliable in practical marine monitoring scenarios due to sparse sampling, missing records, and heterogeneous measurement conditions. To address this limitation, this paper investigates the problem of non-temporal DO prediction, aiming to learn a direct nonlinear mapping between environmental drivers and DO concentration. To explicitly model nonlinear pairwise interaction effects between environmental variables, we propose a Factor-Interaction Neural Network (FINN), which decomposes DO estimation into main effects and structured pairwise interaction effects. This interaction-driven design enhances both representation capacity and interpretability compared with conventional multilayer perceptrons. Furthermore, we develop a physics-informed extension, termed PI-FINN, by incorporating oceanographic-consistent regularization priors that reflect key DO formation mechanisms, including temperature-related solubility behavior, depth-wise smoothness associated with stratification, and chlorophyll-driven biological oxygen production tendencies. To evaluate the physical plausibility of model predictions beyond standard accuracy metrics, we introduce a physics-consistency assessment protocol based on Physics Consistency Violation Rate (PCVR) and its robust variant, and further analyze their convergence stability under different driver-weight configurations. Extensive experiments on a real-world marine dataset demonstrate that FINN achieves competitive predictive accuracy compared with strong machine learning baselines (e.g., SVR, Random Forest, and XGBoost), while the proposed physics-informed design mainly improves the physical consistency, robustness, and interpretability of DO estimation under heterogeneous environmental regimes, although it does not necessarily guarantee superior RMSE or MAE performance compared with purely data-driven models. Specifically, FINN achieves an RMSE of 0.3130, an R2 of 0.9831, and a PCVR of 0.4826 on a dataset composed of key environmental variables, including depth, temperature, salinity, and chlorophyll-a, collected under sparse and irregular sampling conditions. Ablation studies confirm the effectiveness of both factor-interaction modeling and physics-guided regularization components. Overall, the proposed framework further provides a reliable tool for sustainable environmental monitoring by enabling physically consistent dissolved oxygen prediction under sparse observational conditions. Such capability is critical for supporting sustainable water resource management, hypoxia risk assessment, and long-term ecological protection.