GW-RAR-PINN: a novel physics-informed neural network framework for dam-break flow simulation

Physics-informed neural networks (PINNs) have shown potential for modeling open-channel flows; however, their performance deteriorates in dam-break problems due to strong nonlinearities and flow discontinuities. This study proposes a Gradient-Weighted and Residual-based Adaptive Refinement PINN (GW-RAR-PINN), which combines gradient-weighted loss modulation with residual-based adaptive refinement to enhance shock resolution in dam-break flows. One-dimensional dry-bed and wet-bed dam-break problems were simulated to assess the performance of GW-RAR-PINN against the baseline PINN and other representative variants. The results indicate that the proposed GW–RAR–PINN framework achieves the best overall performance among the compared models, with reductions in both MAE and RMSE for water depth and discharge/velocity. For the dry-bed dam-break case, the MAE and RMSE of water depth decrease by 25.2% and 16.0%, respectively, and those of discharge decrease by 38.7% and 26.3%. For the wet-bed case, the MAE and RMSE of water depth decrease by 1.2% and 15.1%, respectively, while the MAE and RMSE of velocity decrease by 4.3% and 18.6%. The GW module reduces the contribution of regions with steep gradients in the loss function, alleviating over-enforcement of governing equations near discontinuities, while the RAR module adaptively enriches collocation points in high-gradient regions to better resolve shock structures. The combined strategy stabilizes network training and improves the representation of localized hydraulic features. These findings demonstrate that GW-RAR-PINN provides a robust and accurate framework for simulating strongly nonlinear dam-break flows.