Engineering Hybrid Physics-Informed Neural Networks for Next-Generation Electricity Systems: A State-of-the-Art Review

TL;DR

This review discusses hybrid physics-informed neural networks for electricity systems, highlighting their ability to improve accuracy, efficiency, and robustness by embedding physical laws into machine learning models.

Contribution

It provides a comprehensive overview of recent hybrid PIML architectures and demonstrates their advantages over purely data-driven models in electricity applications.

Findings

Embedding Maxwell's equations improves predictive accuracy with sparse data.

Hybrid PIML models reduce simulation time significantly compared to finite element methods.

These models outperform purely data-driven approaches in robustness and real-time applications.

Abstract

The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain purely data-driven models. Physics-informed machine learning (PIML) addresses these limitations by embedding governing equations directly into the learning process, yielding accurate, efficient, and scalable solutions for Industry 4.0 applications. This article reviews hybrid PIML architectures for electricity systems, including physics-informed neural networks (PINNs), Deep Operator Networks (DeepONets), Fourier Neural Operators, Extreme Learning Machine-enhanced PINNs, graph-based PINNs (PIGNNs), and domain-decomposition PINNs. Each approach is examined through case studies spanning field analysis, fault detection, digital twins, surrogate modeling, and control optimization. The review shows that embedding Maxwell's equations and other first-principles constraints substantially improves predictive accuracy under sparse and noisy data, reduces simulation time by orders of magnitude relative to finite element methods, and enhances generalization across operating regimes. Hybrid frameworks consistently outperform purely data-driven baselines on parameter sensitivity, dynamic behavior, and robustness, while supporting real-time digital-twin calibration and uncertainty quantification. Persistent challenges include training instability for stiff multi-scale problems, computational cost of high-fidelity models, and the absence of standardized benchmarks. The findings demonstrate that PIML enables a paradigm shift from black-box data-driven methods to transparent, physics-informed strategies, positioning the field for sustained innovation in resilient and intelligent electricity systems.