Physics-Informed Neural Networks for solving 2D Shallow Water Equations: Accuracy Assessment Through Dambreak Benchmark Problems

<title>Abstract</title> <p>This paper evaluates a unified Physics-Informed Neural Network (PINN) framework for simulating dam-break flows governed by the two-dimensional shallow water equations (SWEs). By embedding the continuity and momentum equations directly into the loss function via automatic differentiation, the framework enforces physical consistency without a computational mesh. Four benchmark cases of increasing complexity are considered: a canonical 1D dam-break over wet and dry beds, a 1D dam-break over a triangular hump with transcritical flow and hydraulic jump formation, a 2D partial dam-break with lateral spreading, and a 2D dam-break through a Venturi channel. Predictions are assessed against analytical solutions and experimental measurements. Across all configurations, the model achieves R² values between 0.982 and 0.997, RMSE below 0.01 m, and L2 errors within engineering tolerances. The mesh-free approach proves especially well-suited to geometrically complex domains, positioning PINNs as a practical surrogate for finite-volume solvers in rapid flood risk assessment.</p>