Physics-informed neural networks (PINNs) have shown promise for solving forward and inverse problems in computational mechanics. In this work, we apply a set of state-of-the-art techniques that improve PINNs results such as random Fourier features, random weight factorization, causal training, curriculum learning, and sequence-to-sequence learning [1], [2], combined with the PirateNet architecture [3], to approximate the 2D Shallow Water Equations (SWE). PirateNet, with its adaptive residual connections, enables stable and efficient training of deeper networks, overcoming many limitations of traditional PINNs. As a proof of concept, we successfully applied these methods to benchmark problems, including the 1D and 2D Burgers' equations, achieving relative l2 errors of 2.1% and 1.4% respectively for the u and v velocity fields of the 2D version. These results demonstrate improved convergence and accuracy over standard PINNs in solving highly nonlinear advection-diffusion partial differential equations, particularly those involving shock wave formation. This framework shows great potential for application to the SWE notably by accurately capturing complex hydrodynamic behaviors in large-scale simulations. By leveraging physics-informed constraints and modern machine learning techniques, this work contributes to developing efficient surrogate models for complex fluid dynamics problems, with applications in flood prediction and environmental simulations.