# Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions

arXiv: https://arxiv.org/abs/2205.10129 · HTML: https://mlsanity.com/paper/2205.10129/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 71 references that are in the map.
- First posted on arXiv 16 May 2022.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [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)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [EdgeNets:Edge Varying Graph Neural Networks](https://mlsanity.com/paper/2001.07620/) (2020)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [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)
- [Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks](https://mlsanity.com/paper/1812.09464/) (2018)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [A Convex Neural Network Solver for DCOPF with Generalization Guarantees](https://mlsanity.com/paper/2009.09109/) (2020)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Grid-Graph Signal Processing (Grid-GSP): A Graph Signal Processing Framework for the Power Grid](https://mlsanity.com/paper/2103.06068/) (2021)
- [Learning to Solve Network Flow Problems via Neural Decoding](https://mlsanity.com/paper/2002.04091/) (2020)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)
- [Efficient Identification of Bus Split Events Using Synchrophasor Data](https://mlsanity.com/paper/2010.01296/) (2020)
- [Deep Learning based Model-free Robust Load Restoration to Enhance Bulk System Resilience with Wind Power Penetration](https://mlsanity.com/paper/2109.08074/) (2021)

## Built on by (most cited first, 28 of 28)

- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [PowerGraph-LLM: Novel Power Grid Graph Embedding and Optimization with Large Language Models](https://mlsanity.com/paper/2501.07639/) (2025)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [SafePowerGraph: Safety-aware Evaluation of Graph Neural Networks for Transmission Power Grids](https://mlsanity.com/paper/2407.12421/) (2024)
- [DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks](https://mlsanity.com/paper/2309.12849/) (2023)
- [N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network](https://mlsanity.com/paper/2402.06226/) (2024)
- [Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow](https://mlsanity.com/paper/2206.01864/) (2022)
- [Machine Learning for Scalable and Optimal Load Shedding Under Power System Contingency](https://mlsanity.com/paper/2405.05521/) (2024)
- [Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning](https://mlsanity.com/paper/2406.08917/) (2024)
- [DiffOPF: Diffusion Solver for Optimal Power Flow](https://mlsanity.com/paper/2510.14075/) (2025)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [Wind Power Scenario Generation Using Graph Convolutional Generative Adversarial Network](https://mlsanity.com/paper/2212.10454/) (2022)
- [Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow](https://mlsanity.com/paper/2410.04818/) (2024)
- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [AI Driven Near Real-time Locational Marginal Pricing Method: A Feasibility and Robustness Study](https://mlsanity.com/paper/2306.10080/) (2023)
- [Price-Aware Deep Learning for Electricity Markets](https://mlsanity.com/paper/2308.01436/) (2023)
- [Impact of Data Poisoning Attacks on Feasibility and Optimality of Neural Power System Optimizers](https://mlsanity.com/paper/2502.05727/) (2025)
- [Synthetic Power Flow Data Generation Using Physics-Informed Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2504.17210/) (2025)
- [Residual Correction Models for AC Optimal Power Flow Using DC Optimal Power Flow Solutions](https://mlsanity.com/paper/2510.16064/) (2025)
- [WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers](https://mlsanity.com/paper/2605.05728/) (2026)
- [Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids](https://mlsanity.com/paper/2605.23194/) (2026)
- [FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow](https://mlsanity.com/paper/2607.22788/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)

## Abstract (arXiv)

Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages of our proposed designs include reduced model complexity, improved generalizability and feasibility guarantees. By providing the analytical understanding on the graph subspace stability under grid topology contingency, we show the proposed GNN can quickly adapt to varying grid topology by an efficient re-training strategy. Numerical tests on various test systems of different sizes have validated the prediction accuracy, improved flow feasibility, and topology adaptivity capability of our proposed GNN-based learning framework.