# PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks

arXiv: https://arxiv.org/abs/2311.03415 · HTML: https://mlsanity.com/paper/2311.03415/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE](https://mlsanity.com/paper/1603.01533/) (2016)
- [Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach](https://mlsanity.com/paper/1906.06017/) (2019)
- [Data-Driven Power Flow Linearization: A Regression Approach](https://mlsanity.com/paper/1710.10621/) (2017)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Spatio-Temporal Graph Convolutional Neural Networks for Physics-Aware Grid Learning Algorithms](https://mlsanity.com/paper/2203.16732/) (2022)

## Built on by (most cited first, 21 of 21)

- [PFDelta: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations](https://mlsanity.com/paper/2510.22048/) (2025)
- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [gridfm-datakit-v1: A Python Library for Scalable and Realistic Power Flow and Optimal Power Flow Data Generation](https://mlsanity.com/paper/2512.14658/) (2025)
- [Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator](https://mlsanity.com/paper/2509.22458/) (2025)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)
- [SenseFlow: A Physics-Informed and Self-Ensembling Iterative Framework for Power Flow Estimation](https://mlsanity.com/paper/2505.12302/) (2025)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Parameter-Efficient Domain Adaptation of Physics-Informed Self-Attention based GNNs for AC Power Flow Prediction](https://mlsanity.com/paper/2602.18227/) (2026)
- [Study Design and Demystification of Physics Informed Neural Networks for Power Flow Simulation](https://mlsanity.com/paper/2509.19233/) (2025)
- [Test Time Training for AC Power Flow Surrogates via Physics and Operational Constraint Refinement](https://mlsanity.com/paper/2511.22343/) (2025)
- [Scale-Adaptive Power Flow Analysis with Local Topology Slicing and Multi-Task Graph Learning](https://mlsanity.com/paper/2601.01387/) (2026)
- [Generating adversarial inputs for a graph neural network model of AC power flow](https://mlsanity.com/paper/2602.17975/) (2026)
- [PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow with Continual Learning](https://mlsanity.com/paper/2603.16879/) (2026)
- [BOOST-RPF: Boosted Sequential Trees for Radial Power Flow](https://mlsanity.com/paper/2603.21977/) (2026)
- [Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids](https://mlsanity.com/paper/2605.23194/) (2026)
- [Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening](https://mlsanity.com/paper/2607.12241/) (2026)
- [Unified Heterogeneous Graph Neural Network solver for Power Flow, Optimal Power Flow and State Estimation](https://mlsanity.com/paper/2609.16738/) (2026)
- [Hierarchical GNNs for power flow: letting physics shape the hierarchy](https://mlsanity.com/paper/2609.26603/) (2026)
- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)
- [Learning by Examples: Power Grid Steady State Analysis with a Tabular Foundation Model](https://mlsanity.com/paper/2610.20462/) (2026)

## Abstract (arXiv)

Accurate and efficient power flow (PF) analysis is crucial in modern electrical networks' operation and planning. Therefore, there is a need for scalable algorithms that can provide accurate and fast solutions for both small and large scale power networks. As the power network can be interpreted as a graph, Graph Neural Networks (GNNs) have emerged as a promising approach for improving the accuracy and speed of PF approximations by exploiting information sharing via the underlying graph structure. In this study, we introduce PowerFlowNet, a novel GNN architecture for PF approximation that showcases similar performance with the traditional Newton-Raphson method but achieves it 4 times faster in the simple IEEE 14-bus system and 145 times faster in the realistic case of the French high voltage network (6470rte). Meanwhile, it significantly outperforms other traditional approximation methods, such as the DC relaxation method, in terms of performance and execution time; therefore, making PowerFlowNet a highly promising solution for real-world PF analysis. Furthermore, we verify the efficacy of our approach by conducting an in-depth experimental evaluation, thoroughly examining the performance, scalability, interpretability, and architectural dependability of PowerFlowNet. The evaluation provides insights into the behavior and potential applications of GNNs in power system analysis.