###### Abstract
By enforcing physical consistency, PINNs can generalize better in data-scarce settings, yielding solutions that conform to known operational constraints even in the absence of extensive labeled datasets [13]. Originally developed for solving partial differential equations in fluid mechanics and continuum physics, PINNs have been successfully adapted for several power system tasks. In the domain of power system dynamics and stability, PINNs have been applied to transient stability analysis, offering computational advantages over traditional numerical integration methods [13; 14]. In the realm of power flow analysis, PINNs have shown promise for accelerating AC power flow calculations. A study by [PERSON] et al. [11] proposed an improved PINN-based AC power flow model for distribution networks that incorporates physical line losses, resulting in higher accuracy and increased learning potential. The authors demonstrated that their physics-informed approach outperformed conventional methods and exhibited strong prediction capabilities for scenarios outside the training set, addressing a substantial deficiency of purely model-free techniques. The recent literature has increasingly focused on integrating physical modeling with machine learning to enhance SE in power systems [15]. PINNs have been explored for power systems by researchers like [PERSON] et al. [16], who demonstrated that embedding the AC power flow equations into neural networks enables better generalization under sparse measurement conditions. [PERSON] et al. [2] proposed a PINN framework for accelerating state estimation tasks in distribution systems, reducing convergence time while maintaining physical consistency. The study demonstrated impressive results, achieving up to an 11% increase in accuracy, 75% reduction in the standard deviation of results, and 30% faster convergence, as validated through comprehensive experiments on the IEEE 14-bus system. Similarly, in [17], [PERSON] and [PERSON] introduced physics-aware models that maintain observability even with limited data, addressing challenges typical in real-world networks. [PERSON] et al. [18] further advanced this line of work by proposing a decentralized pruned physics-aware neural network (D-P2N2), which combines physical topology information and decentralized learning to improve scalability, computational efficiency, and accuracy in large-scale distribution grids. Other approaches, such as those by [PERSON] et al. [19], highlight the ability of PINNs to maintain robustness under partial observability and measurement noise. These methods represent a shift from black-box learning to hybrid modeling, leveraging prior knowledge to mitigate overfitting and improve extrapolation in unseen operational regimes [20]. Graph-based architectures have also emerged as powerful tools for modeling electrical networks [21]. [PERSON] et al. [22] and [PERSON] et al. [8] developed message-passing neural networks tailored for power flow problems, capturing network topology and improving accuracy in both state estimation and power flow prediction. Building on this, [PERSON] and [PERSON] [23] introduced Physics-Informed Graphical Neural Networks (PIGNNs) that incorporate [PERSON]'s laws directly into graph-based architectures, improving reliability in low-measurement regimes. More recently, [PERSON] et al. [24] proposed a hybrid GNN-PINN framework for three-phase unbalanced systems, offering improved scalability and accuracy in complex distribution networks. These advances collectively demonstrate that combining physical laws with deep learning not only addresses the limitations of purely data-driven models--such as lack of physical interpretability and poor generalization--but also provides a promising foundation for state estimation in increasingly complex and unbalanced distribution systems. Despite the promising progress in recent studies, several critical research gaps remain in the application of PINNs to distribution system state estimation.