Adaptive Weighted Multi-Physics-Informed Neural Network for High-Accuracy Shock Wave Capturing

In recent years, physics-informed neural network (PINN) has gained attention as a novel approach for solving partial differential equations. By embedding physical constraints, such as conservation laws and boundary conditions, into the loss function, the model’s adaptability to physical problems is enhanced, yielding more precise solutions. However, PINN often produces smooth results, making it challenging to solve problems involving strong discontinuities like shock wave. To improve the accuracy of PINN in capturing shocks, this paper proposes an adaptive weighted multi-physics-informed neural network (AW-MPINN). To address numerical instability and convergence issues caused by gradient imbalance among constraint terms during training, the weights of these terms are dynamically optimized based on gradient variations, enabling the model to flexibly respond to changes and balance loss contributions in discontinuous regions. Additionally, weight coefficients are constrained using gradient clipping to reduce optimization bias caused by weight fluctuations. The proposed AW-MPINN is evaluated on three benchmark problems. Compared to nonadaptive methods, it achieves sharper discontinuity resolution and improved accuracy under limited training data; when tested against existing adaptive approaches, it demonstrates faster convergence and more stable loss balancing, leading to enhanced robustness and shock-capturing capability.