Physics-informed neural networks (PINNs) have emerged as a framework for solving partial differential equations by embedding governing physical laws directly into the neural network training process. Despite their growing success, standard PINN formulations rely primarily on loss functions based on mean squared or absolute error, which inherently average residuals over the computational domain. As a result, these losses can overlook localized regions with sharp gradients, strong nonlinearities, or discontinuities, often leading to inaccurate or unstable solutions in such critical areas. To address this limitation, we introduce a novel loss formulation that augments the traditional mean-based loss with an additional variance-based term, computed as the standard deviation of the residuals. This enhancement promotes a more uniform distribution of residuals throughout the domain and encourages the network to better capture localized physical behaviors. The proposed variance-enhanced loss is simple to implement, and introduces negligible computational overhead. We assess the effectiveness of the method on a diverse set of challenging problems, including Burgers’ problem and steady Navier–Stokes flows. Across all cases, the proposed approach consistently improves solution accuracy, reduces maximum error, and yields more homogeneous residual fields when compared to conventional PINN loss functions. These results demonstrate that variance-based regularization provides a robust strategy for enhancing the reliability and performance of PINNs in complex, real-world physics applications.