Mechanism-Based Insights and Ablation Study of Multi-Constraint Strategies for Physics-Informed Neural Networks in Shock-Dominated Dam-Break Flows

Abstract

Physics-informed neural networks (PINNs) provide mesh-free approximation and rapid inference for dam-break flood simulations. However, the effectiveness and underlying mechanisms of different enhancement strategies for engineering-representative shock-dominated flows remain insufficiently understood. To address this issue, this study established a controlled ablation framework based on the one-dimensional shallow water equations, using an instantaneous full dam-break scenario with engineering-representative conditions constructed from the actual dam height parameters of the Chaole Reservoir in China. Under identical network architecture and training configuration, the performance and mechanisms of three representative PINN enhancement strategies, namely sparse data supervision, Sobolev gradient matching, and adaptive shock weighting, were systematically investigated. The results indicate that sparse data supervision is the primary contributor to performance improvement, significantly reducing prediction error while improving the accuracy of shock-front localization and local flow-field prediction. In contrast, fixed-weight Sobolev gradient matching provides only limited improvement in global prediction accuracy and fails to enhance the prediction of local extrema in the shock region, which is associated with its modification of the partial differential equation (PDE) loss landscape by reducing the low-residual optimization region. Adaptive shock weighting provides only marginal additional benefits and does not substantially improve the performance of the strong-form PINN for discontinuous problems. The combined ablation, loss landscape, and weight sensitivity analyses demonstrate that, under the adopted supervision density and strong-form PINN configuration, incorporating a limited set of high-quality sparse supervisory observations with the adopted spatial sampling strategy provides a substantially larger accuracy improvement than the additional PDE-based regularization mechanisms investigated in this study. This study provides controlled attribution of representative PINN enhancement strategies and offers reproducible methodological insights for their evaluation in shock-dominated shallow water flows.