A Physics-Coupled Deep Learning Framework for Hydrodynamic Diffusion Modeling in Watershed Systems: Integrating Spatiotemporal Networks and Environmental Constraints

The modeling and simulation of complex spatiotemporal systems are crucial for understanding and solving multidimensional dynamical systems, particularly in earth and environmental sciences. Accurate comprehension and computational modeling of fluid transport, environmental processes, and substance diffusion depend heavily on solving governing equations. Despite significant advancements in artificial intelligence techniques, such as deep learning and neural operator methods, challenges persist regarding robustness, scalability, and adherence to physical laws in hydrodynamic systems. This paper introduces a multi-scale interdisciplinary hybrid learning framework that integrates physics-informed neural networks with neural operator-based deep learning techniques to model hydrodynamic transport processes. By incorporating convolutional neural networks for multi-scale feature extraction and implementing hard constraints to enforce physical boundary conditions, the proposed framework enhances the stability and accuracy of predictions in dynamic fluid systems. The approach facilitates efficient reconstruction of spatiotemporal characteristics and parameterized dynamics while ensuring physical consistency. Through case studies of two-dimensional solute diffusion equations, the framework demonstrates superior generalizability and robustness in addressing high-dimensional and nonlinear fluid systems. Comparative experiments with multiple baseline models highlight significant improvements in prediction accuracy, noise resistance, and adaptability to sparse datasets. The proposed method effectively addresses limitations of traditional data-driven approaches by integrating domain-specific physical principles, providing a reliable and high-fidelity solution for hydrodynamic modeling and environmental system monitoring. This research offers a transformative approach to feature extraction, dynamic representation, and physically consistent modeling of complex spatiotemporal systems.