Solving complex flood wave propagation using split Coefficient-based Physical Informed Neural Network

Abstract

To address complex flood wave propagation problems characterized by discontinuity and anisotropic superposition, Split Coefficient-based Physical Informed Neural Network (SC-PINN) is proposed. The Split Coefficient (SC) strategy is employed to decompose the spatial features of flood waves along different propagation directions. Spatial derivatives, matching each spatial feature component, are obtained through the Taylor series, ensuring that each component contains only the information of waves propagating in a single positive or negative direction. This approach captures flow characteristics in each direction, thereby reducing the spectral bias encountered by PINN when learning complex flow regimes during flood wave propagation. To verify the effectiveness and accuracy, the proposed SC-PINN is applied to three classical dam-break scenarios. Additionally, an investigation is conducted into why the SC strategy assists PINN in improving the accuracy of flood forecasting. The results indicate that as the changing rate in water depth increases, the flow characteristics of asymmetric propagation and superposition become more pronounced, which leads to PINN failing to capture the complex flow regime effectively. In contrast, the proposed SC-PINN splits the total changing rate in water depth along different propagation directions, enabling the network model to independently learn the changing rate component in water depth in each direction. Consequently, the new method accurately captures not only the strong discontinuity regions in shallow water flow but also the phenomena of double shock system, vortex, and wake formed by the interaction between flood waves and obstacles. Furthermore, the proposed approach successfully describes asymmetric flow around the dam breach and local high-water levels induced by irregular breaches. It provides a potent solution for addressing complex flood wave propagation problems characterized by discontinuity and anisotropic superposition.