Learning Without Adversarial Training: A Physics-Informed Neural Network for Secure Power System State Estimation under False Data Injection Attacks

arXiv cs.LG / 4/28/2026

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Key Points

The paper introduces a Physics-Informed Neural Network (PINN) for power system state estimation (PSSE) that improves robustness against stealth-constrained AC false data injection attacks (FDIAs).
Unlike prior PINN methods, the proposed model is trained without adversarial training by using a dynamic loss-weighting scheme based on homoscedastic uncertainty to balance data-fit and physics-residual terms.
The approach embeds power-flow consistency into the learning objective and aims to reduce dependence on manually tuned weight hyperparameters during training.
Robustness is evaluated on the IEEE 118-bus benchmark against multiple representative stealthy-FDIA attack types, and performance is quantified with Mean Absolute Error (MAE) for voltage magnitudes and phase angles.
Experimental results show the method achieves higher accuracy and greater training/inference stability than fixed-weight PINN baselines under the tested attack scenarios.

Abstract

State estimation is a cornerstone of power system control-center operations, and its robust operation is increasingly a cyber-physical security concern as modern grids become more digitalized and communication-intensive. Neural network-based approaches have gained attention as alternatives to conventional model-based state estimation methods. Physics-Informed Neural Networks (PINNs), which embed power-flow consistency into the learning objective, have shown improved accuracy over existing approaches. This work proposes a PINN-based model for Power System State Estimation (PSSE) that protects the estimation process against the stealth-constrained AC False Data Injection Attacks (FDIAs) considered in this study. The model is developed without adversarial training. Instead, a dynamic loss-weighting formulation based on homoscedastic uncertainty learns the relative scaling of supervised data-fit and physics-residual terms during training, reducing sensitivity to manual weight tuning. Robustness is evaluated on the IEEE 118-bus system using representative stealthy-FDIA families including state distortion, load redistribution, line overloading, and residual-constrained stealth corruption. Performance is measured using Mean Absolute Error (MAE) on voltage magnitudes and phase angles. Results demonstrate higher accuracy and stability than existing fixed-weight PINN variants.