This paper addresses the issues of accuracy and efficiency degradation in solving partial differential equations using physics-informed deep learning. It points out that existing methods exhibit significant differences in the convergence speeds of residuals at different training points, and that this difference leads to the slowest convergence speed dominating the overall convergence speed. To address this issue, this paper proposes a pointwise adaptive weighting method that balances the residual decay speeds across training points. The proposed method is compared and analyzed with existing state-of-the-art adaptive weighting methods, demonstrating superior performance on both physics-informed neural networks and physics-informed deep operator networks. Specifically, it demonstrates the advantages of limited weights, high prediction accuracy, fast convergence, low training uncertainty, low computational cost, and easy hyperparameter tuning.
