mlsanityData to 7 Oct 2026

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

arXiv 1909.10461 ↗First posted 19 Sep 2019eess.SP cs.AI cs.LGcited by 93

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Abstract (arXiv)

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often needed to be solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the prior states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of widely adopted OPF linear DC approximation by at least two orders of magnitude.

Key facts. Cited by 93 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Sep 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 17; 2022: 13; 2023: 20; 2024: 13; 2025: 15; 2026: 15.

93 papers.

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  1. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  2. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  3. 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 52
  4. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  5. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  6. 2021Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimizationcited by 31
  7. 2021Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatchcited by 29
  8. 2024CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbationscited by 27
  9. 2021Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networkscited by 26
  10. 2021Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flowcited by 23
  11. 2024OPFData: Large-scale datasets for AC optimal power flow with topological perturbationscited by 22
  12. 2021Learning Hard Optimization Problems: A Data Generation Perspectivecited by 21
38 more
  1. 2021Leveraging power grid topology in machine learning assisted optimal power flowcited by 21
  2. 2021Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Methodcited by 20
  3. 2021OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasetscited by 17
  4. 2021Spatial Network Decomposition for Fast and Scalable AC-OPF Learningcited by 15
  5. 2022Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitmentscited by 12
  6. 2023Compact Optimization Learning for AC Optimal Power Flowcited by 11
  7. 2023Dual Conic Proxies for AC Optimal Power Flowcited by 11
  8. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  9. 2021A Review of Physics-based Machine Learning in Civil Engineeringcited by 9
  10. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  11. 2021Data-Driven Time Series Reconstruction for Modern Power Systems Researchcited by 7
  12. 2022Risk-Aware Control and Optimization for High-Renewable Power Gridscited by 7
  13. 2022Learning Regionally Decentralized AC Optimal Power Flows with ADMMcited by 7
  14. 2023Learning Optimal Power Flow Value Functions with Input-Convex Neural Networkscited by 7
  15. 2026LUMINA: Foundation Models for Topology Transferable ACOPFcited by 7
  16. 2021Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problemscited by 6
  17. 2022Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Supportcited by 6
  18. 2024Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programmingcited by 6
  19. 2025Towards Generalization of Graph Neural Networks for AC Optimal Power Flowcited by 5
  20. 2023Two-Stage Learning For the Flexible Job Shop Scheduling Problemcited by 4
  21. 2023Data-driven decision-focused surrogate modelingcited by 4
  22. 2023Predict-Then-Optimize by Proxy: Learning Joint Models of Prediction and Optimizationcited by 4
  23. 2023Multi-dimensional Fair Federated Learningcited by 4
  24. 2024Dual Interior Point Optimization Learningcited by 4
  25. 2025Towards graph neural networks for provably solving convex optimization problemscited by 4
  26. 2025PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planningcited by 4
  27. 2022Bucketized Active Sampling for Learning ACOPFcited by 3
  28. 2022AutoML for Climate Change: A Call to Actioncited by 3
  29. 2022Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Dualitycited by 3
  30. 2022Minimizing Worst-Case Violations of Neural Networkscited by 3
  31. 2023Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generationcited by 3
  32. 2023Optimization-based Learning for Dynamic Load Planning in Trucking Service Networkscited by 3
  33. 2023Achieving Constraints in Neural Networks: A Stochastic Augmented Lagrangian Approachcited by 3
  34. 2023Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flowcited by 3
  35. 2024Learning to Solve the Constrained Most Probable Explanation Task in Probabilistic Graphical Modelscited by 3
  36. 2022Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flowcited by 2
  37. 2023Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimizationcited by 2
  38. 2023On The Fairness Impacts of Hardware Selection in Machine Learningcited by 2

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