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

arXiv: https://arxiv.org/abs/2604.22784 · HTML: https://mlsanity.com/paper/2604.22784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [Physics-informed Graphical Neural Network for Power System State Estimation](https://mlsanity.com/paper/2312.17738/) (2023)
- [Physics-Informed Deep Neural Network Method for Limited Observability State Estimation](https://mlsanity.com/paper/1910.06401/) (2019)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [Physics-Informed Neural Networks in Power System Dynamics: Improving Simulation Accuracy](https://mlsanity.com/paper/2501.17621/) (2025)
- [Enhancement of Distribution System State Estimation Using Pruned Physics-Aware Neural Networks](https://mlsanity.com/paper/2102.03893/) (2021)
- [Estimate Three-Phase Distribution Line Parameters With Physics-Informed Graphical Learning Method](https://mlsanity.com/paper/2102.09023/) (2021)
- [AC False Data Injection Attacks in Power Systems: Design and Optimization](https://mlsanity.com/paper/2406.06988/) (2024)

## Abstract (arXiv)

Power System State Estimation (PSSE) converts geographically distributed measurements into the voltage magnitudes and phase angles needed for grid monitoring and control. Learned estimators can perform this mapping rapidly, but model-aware False Data Injection Attacks (FDIAs) may corrupt their inputs while retaining AC plausibility and residual-based stealth. Physics-Informed Neural Networks (PINNs) limit candidate states through power-flow consistency; however, their robustness depends on balancing supervised and physics losses whose scales and gradient contributions evolve during training. This paper proposes a PINN that jointly learns homoscedastic uncertainty parameters and uses them to adapt the two objectives. The formulation assigns trainable log-uncertainties to the active-power, reactive-power, voltage, and angle losses while safeguarding against an underweighted physics objective. The estimator is trained only on clean steady-state data and is evaluated, without adversarial retraining, under baseline state-distortion and stricter residual-profile-matching regimes on the IEEE~118-bus system. Accuracy is measured against the uncompromised system state. Relative to a fixed-weight PINN, dynamic weighting reduces overall Mean Absolute Error (MAE) by 55% while also improving voltage- and angle-estimation accuracy. The results show that learning the physics/data balance from clean data improves robustness to unseen FDIAs.