WINN: A PDE Residual Loss-Free Network for Homogeneous Long-Time Wave Problems

Physics-informed neural networks (PINNs) struggle to solve wave equations over long temporal domains. In this work, we investigate the sources of this failure and introduce WINN (Wave-Informed Neural Network), a novel neural architecture that incorporates the analytical structure of the wave equation directly into the model. WINN satisfies the homogeneous wave equation with constant wave speed exactly by construction, eliminating the need for a PDE residual loss and allowing training to focus solely on the initial and boundary conditions. We show through extensive experiments that WINN remains accurate across long-time wave problems with different frequencies, spatial dimensions, wave speeds, and domain geometries, achieving $7$–$86\times$ lower relative $L_2$ error than the best-performing baseline. WINN achieves training times that are slightly shorter than Vanilla PINN in 2D and 1.7$\times$ faster than FBPINN in 3D. These results demonstrate that incorporating the governing PDE structure directly into the neural representation can substantially improve the accuracy and robustness of neural solvers for long-time wave dynamics.