arXiv:2611.14240v1 Announce Type: new Abstract: Recent advances in artificial deep learning-based power flow (PF) solvers have primarily focused on improving estimation accuracy, while their physical feasibility and operational reliability under realistic system variations remain insufficiently evaluated. This paper proposes a physics-informed evaluation framework for deep learning-based PF solvers under topology and load distribution shifts. Beyond conventional voltage-domain errors, the framework incorporates KCL gaps, branch-flow gaps, KVL residuals, continuous feasibility scores, and strict, practical, and relaxed PF feasibility rates. Four case studies are designed to investigate topology shifts, mixed topology training, load distribution shifts, and combined topology distribution shifts. Eight ANN architectures, including graph input models, load-only baselines, and physics-informed neural networks, are evaluated under consistent settings. The results demonstrate that low estimation errors do not necessarily correspond to physically feasible or operationally reliable PF solutions, particularly under combined system shifts. The proposed framework establishes an initial foundation and analysis for the development and verification of trustworthy deep learning-based PF solvers, providing support for their reliable deployment in future AI-enabled power system analysis.