# Physics-Informed Machine Learning for Data Anomaly Detection, Classification, Localization, and Mitigation: A Review, Challenges, and Path Forward

arXiv: https://arxiv.org/abs/2309.10788 · HTML: https://mlsanity.com/paper/2309.10788/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2023.

## Built on by (most cited first, 8 of 8)

- [A Scoping Review of Machine Learning Applications in Power System Protection and Disturbance Management](https://mlsanity.com/paper/2509.09053/) (2025)
- [Physics-Informed Convolutional Autoencoder for Cyber Anomaly Detection in Power Distribution Grids](https://mlsanity.com/paper/2312.04758/) (2023)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [An Unsupervised Adversarial Autoencoder for Cyber Attack Detection in Power Distribution Grids](https://mlsanity.com/paper/2404.02923/) (2024)
- [Multivariate Physics-Informed Convolutional Autoencoder for Anomaly Detection in Power Distribution Systems with High Penetration of DERs](https://mlsanity.com/paper/2406.02927/) (2024)
- [Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation](https://mlsanity.com/paper/2508.21559/) (2025)
- [Integrated Simulation Framework for Adversarial Attacks on Autonomous Vehicles](https://mlsanity.com/paper/2509.05332/) (2025)
- [The Enhanced Physics-Informed Kolmogorov-Arnold Networks: Applications of Newton's Laws in Financial Deep Reinforcement Learning (RL) Algorithms](https://mlsanity.com/paper/2602.01388/) (2026)

## Abstract (arXiv)

Advancements in digital automation for smart grids have led to the installation of measurement devices like phasor measurement units (PMUs), micro-PMUs (μ-PMUs), and smart meters. However, a large amount of data collected by these devices brings several challenges as control room operators need to use this data with models to make confident decisions for reliable and resilient operation of the cyber-power systems. Machine-learning (ML) based tools can provide a reliable interpretation of the deluge of data obtained from the field. For the decision-makers to ensure reliable network operation under all operating conditions, these tools need to identify solutions that are feasible and satisfy the system constraints, while being efficient, trustworthy, and interpretable. This resulted in the increasing popularity of physics-informed machine learning (PIML) approaches, as these methods overcome challenges that model-based or data-driven ML methods face in silos. This work aims at the following: a) review existing strategies and techniques for incorporating underlying physical principles of the power grid into different types of ML approaches (supervised/semi-supervised learning, unsupervised learning, and reinforcement learning (RL)); b) explore the existing works on PIML methods for anomaly detection, classification, localization, and mitigation in power transmission and distribution systems, c) discuss improvements in existing methods through consideration of potential challenges while also addressing the limitations to make them suitable for real-world applications.