# Leveraging power grid topology in machine learning assisted optimal power flow

arXiv: https://arxiv.org/abs/2110.00306 · HTML: https://mlsanity.com/paper/2110.00306/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 53 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations](https://mlsanity.com/paper/1711.01728/) (2017)
- [Learning Warm-Start Points for AC Optimal Power Flow](https://mlsanity.com/paper/1905.08860/) (2019)
- [Learning for DC-OPF: Classifying active sets using neural nets](https://mlsanity.com/paper/1902.05607/) (2019)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence](https://mlsanity.com/paper/1405.0766/) (2014)
- [Solutions of DC OPF are Never AC Feasible](https://mlsanity.com/paper/1912.00319/) (2019)
- [Learning an Optimally Reduced Formulation of OPF through Meta-optimization](https://mlsanity.com/paper/1911.06784/) (2019)
- [Hot-Starting the Ac Power Flow with Convolutional Neural Networks](https://mlsanity.com/paper/2004.09342/) (2020)
- [Implied Constraint Satisfaction in Power System Optimization: The Impacts of Load Variations](https://mlsanity.com/paper/1904.01757/) (2019)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Stochastic AC Optimal Power Flow: A Data-Driven Approach](https://mlsanity.com/paper/1910.09144/) (2019)

## Built on by (most cited first, 22 of 22)

- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network](https://mlsanity.com/paper/2402.06226/) (2024)
- [Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning](https://mlsanity.com/paper/2406.08917/) (2024)
- [Learning-based AC-OPF Solvers on Realistic Network and Realistic Loads](https://mlsanity.com/paper/2205.09452/) (2022)
- [Machine Learning for Electricity Market Clearing](https://mlsanity.com/paper/2205.11641/) (2022)
- [Multi-fidelity power flow solver](https://mlsanity.com/paper/2205.13362/) (2022)
- [Graph neural networks for power grid operational risk assessment under evolving grid topology](https://mlsanity.com/paper/2405.07343/) (2024)
- [SenseFlow: A Physics-Informed and Self-Ensembling Iterative Framework for Power Flow Estimation](https://mlsanity.com/paper/2505.12302/) (2025)
- [Large Language Models for Power System Security: A Novel Multi-Modal Approach for Anomaly Detection in Energy Management Systems](https://mlsanity.com/paper/2508.10044/) (2025)
- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier](https://mlsanity.com/paper/2310.08601/) (2023)
- [Residual Correction Models for AC Optimal Power Flow Using DC Optimal Power Flow Solutions](https://mlsanity.com/paper/2510.16064/) (2025)
- [Optimizing Energy Management of Smart Grid using Reinforcement Learning aided by Surrogate models built using Physics-informed Neural Networks](https://mlsanity.com/paper/2510.17380/) (2025)
- [Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee](https://mlsanity.com/paper/2512.11127/) (2025)
- [Graph Machine Learning: An Opportunity for Power Systems](https://mlsanity.com/paper/2608.16494/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)
- [Learning by Examples: Power Grid Steady State Analysis with a Tabular Foundation Model](https://mlsanity.com/paper/2610.20462/) (2026)

## Abstract (arXiv)

Machine learning assisted optimal power flow (OPF) aims to reduce the computational complexity of these non-linear and non-convex constrained optimization problems by consigning expensive (online) optimization to offline training. The majority of work in this area typically employs fully connected neural networks (FCNN). However, recently convolutional (CNN) and graph (GNN) neural networks have also been investigated, in effort to exploit topological information within the power grid. Although promising results have been obtained, there lacks a systematic comparison between these architectures throughout literature. Accordingly, we introduce a concise framework for generalizing methods for machine learning assisted OPF and assess the performance of a variety of FCNN, CNN and GNN models for two fundamental approaches in this domain: regression (predicting optimal generator set-points) and classification (predicting the active set of constraints). For several synthetic power grids with interconnected utilities, we show that locality properties between feature and target variables are scarce and subsequently demonstrate marginal utility of applying CNN and GNN architectures compared to FCNN for a fixed grid topology. However, with variable topology (for instance, modeling transmission line contingency), GNN models are able to straightforwardly take the change of topological information into account and outperform both FCNN and CNN models.