Solving the two-dimensional Shallow Water Equations (SWE) is a fundamental problem in flood simulation; however, the presence of discontinuities such as shock waves poses significant challenges for numerical analysis. In recent years, physics-informed neural networks (PINNs) have emerged as a promising approach for solving SWE due to their advantages in parallel computation, data assimilation, and parameter calibration. Despite these benefits, conventional PINNs struggle with discontinuous solutions, primarily because automatic differentiation fails to accurately represent derivatives at shock locations. In this study, we employ a “retreat to advance” strategy to alleviate this limitation by redirecting the model’s learning focus from discontinuous regions to smooth solution domains. Specifically, a gradient-based indicator is used to detect shock regions, and their contribution to the physics residual is adaptively reduced. This weighting strategy allows the PINN to prioritize smooth regions during training, thereby naturally inducing physically consistent discontinuities without explicitly modeling shock structures. Furthermore, to preserve the conservation properties across discontinuities, the proposed PINN-WE framework incorporates Rankine–Hugoniot (RH) conditions derived from the weak formulation of conservation laws as localized constraints near shock regions. This hybrid strategy improves the robustness and physical consistency of PINN-based solutions for discontinuous SWE problems, demonstrating its potential for reliable flood simulation applications.