Abstract
The real-time forecasting of flood dynamics is a long-standing challenge traditionally addressed through numerical solutions of the Shallow Water Equations (SWEs). Numerical solutions of realistic flow problems using numerical schemes are often hindered by high computational costs, particularly due to the need for fine spatial and temporal discretization, complex boundary conditions, and the resolution of non-linearities inherent in the governing equations. In this study, we investigate the use of Physics-Informed Neural Networks (PINNs) to solve 1D and 2D SWEs in dam-break scenarios. The proposed PINN framework incorporates the governing partial differential equations along with the initial and boundary conditions directly within the training process of the network, ensuring physically consistent solutions. We conduct a systematic comparison of the solutions of SWE using the classical numerical scheme (Lax-Wendroff) with estimates of physics informed neural networks. For 1D SWE, a neural network is trained and validated on a dam-break problem, revealing that physics-informed models produce smoother but still acceptable estimates of wave propagation compared to standard numerical results. For 2D SWE, we consider various configurations of dam geometries along with varying initial profiles for water heights. Across all scenarios, reproduce the numerical baselines, albeit with limited accuracy, while avoiding spurious oscillations and numerical artifacts. Further tuning, achieved by incorporating numerical solutions into the PINN training, improved accuracy. This proof of concept demonstrates the potential of hybridized PINNs as a mesh-free, scalable, and generalizable framework for approximating solutions to nonlinear hyperbolic systems. Our results indicate that pre-trained, physics-informed models could serve as a viable alternative for real-time flood forecasting in complex domains.