# Power to the Relational Inductive Bias: Graph Neural Networks in Electrical Power Grids

arXiv: https://arxiv.org/abs/2109.03604 · HTML: https://mlsanity.com/paper/2109.03604/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 8 Sep 2021.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks](https://mlsanity.com/paper/1812.09464/) (2018)
- [Integrating Logical Rules Into Neural Multi-Hop Reasoning for Drug Repurposing](https://mlsanity.com/paper/2007.05292/) (2020)

## Built on by (most cited first, 18 of 18)

- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [What functions can Graph Neural Networks compute on random graphs? The role of Positional Encoding](https://mlsanity.com/paper/2305.14814/) (2023)
- [GNN at the Edge: Cost-Efficient Graph Neural Network Processing over Distributed Edge Servers](https://mlsanity.com/paper/2210.17281/) (2022)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Graph Reinforcement Learning for Power Grids: A Comprehensive Survey](https://mlsanity.com/paper/2407.04522/) (2024)
- [PFDelta: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations](https://mlsanity.com/paper/2510.22048/) (2025)
- [Efficient Model-Stealing Attacks Against Inductive Graph Neural Networks](https://mlsanity.com/paper/2405.12295/) (2024)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [Graph Neural Networks for Electric and Hydraulic Data Fusion to Enhance Short-term Forecasting of Pumped-storage Hydroelectricity](https://mlsanity.com/paper/2404.03368/) (2024)
- [Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning](https://mlsanity.com/paper/2406.08917/) (2024)
- [Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions](https://mlsanity.com/paper/2407.12419/) (2024)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Node Embedding for Homophilous Graphs with ARGEW: Augmentation of Random walks by Graph Edge Weights](https://mlsanity.com/paper/2308.05957/) (2023)
- [Flow-Attentional Graph Neural Networks](https://mlsanity.com/paper/2506.06127/) (2025)
- [Parameter-Efficient Domain Adaptation of Physics-Informed Self-Attention based GNNs for AC Power Flow Prediction](https://mlsanity.com/paper/2602.18227/) (2026)
- [Graph Machine Learning: An Opportunity for Power Systems](https://mlsanity.com/paper/2608.16494/) (2026)
- [A Comparative Study of Graph Representations for GNN-Based Power Grid Control in L2RPN](https://mlsanity.com/paper/2609.02538/) (2026)

## Abstract (arXiv)

The application of graph neural networks (GNNs) to the domain of electrical power grids has high potential impact on smart grid monitoring. Even though there is a natural correspondence of power flow to message-passing in GNNs, their performance on power grids is not well-understood. We argue that there is a gap between GNN research driven by benchmarks which contain graphs that differ from power grids in several important aspects. Additionally, inductive learning of GNNs across multiple power grid topologies has not been explored with real-world data. We address this gap by means of (i) defining power grid graph datasets in inductive settings, (ii) an exploratory analysis of graph properties, and (iii) an empirical study of the concrete learning task of state estimation on real-world power grids. Our results show that GNNs are more robust to noise with up to 400% lower error compared to baselines. Furthermore, due to the unique properties of electrical grids, we do not observe the well known over-smoothing phenomenon of GNNs and find the best performing models to be exceptionally deep with up to 13 layers. This is in stark contrast to existing benchmark datasets where the consensus is that 2 to 3 layer GNNs perform best. Our results demonstrate that a key challenge in this domain is to effectively handle long-range dependence.