Modeling Hydrodynamic Diffusion Processes using Spatio-Temporal Deep Neural Networks with Environmental Physical-Coupled Constraints

The simulation and analysis of complex spatiotemporal systems are crucial for expressing and solving chaotic dynamical systems such as those in Earth and environmental sciences. Understanding and computing physical processes, re-actions, or substance transport typically relies on control equations. This paper aims to explore a novel research paradigm by enhancing the physical network coupling structure to construct predictive models for fluid dynamics systems, simulating spatiotemporal dynamical processes of substance transformation in the domain of environmental physics. In particular, when addressing problems involving the non-homogeneous 2D fluid dynamics equations, the characteristic parameters of the phys-ical processes were redefined. This was achieved by encoding hard boundary conditions and designing appropriate neural network architectures to mitigate over-fitting issues during the prediction of parameterized dynamical systems. Comparative experiments involving five benchmark physics-informed neural network methods emphasize the significant improvement in capturing time-varying features and prediction accuracy brought by the proposed approach. Through various water cycle scenarios, the model's estimation ability for diffusion fields is validated, focusing on analyzing the influence of data errors and sample size on the computational results of this deep neural network. Notably, the proposed method exhibits higher robustness to outlier observations under extreme conditions.