# Learning for DC-OPF: Classifying active sets using neural nets

arXiv: https://arxiv.org/abs/1902.05607 · HTML: https://mlsanity.com/paper/1902.05607/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2019.

## Built on by (most cited first, 30 of 31)

- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [On Representing Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2209.12288/) (2022)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments](https://mlsanity.com/paper/2211.15755/) (2022)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [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)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [Scalable Learning for Optimal Load Shedding Under Power Grid Emergency Operations](https://mlsanity.com/paper/2111.11980/) (2021)
- [PowerGNN: A Topology-Aware Graph Neural Network for Electricity Grids](https://mlsanity.com/paper/2503.22721/) (2025)
- [Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow](https://mlsanity.com/paper/2405.06109/) (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)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees](https://mlsanity.com/paper/2304.01409/) (2023)
- [Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks](https://mlsanity.com/paper/2311.13949/) (2023)
- [Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming](https://mlsanity.com/paper/2506.05567/) (2025)
- [Towards Understanding the Unreasonable Effectiveness of Learning AC-OPF Solutions](https://mlsanity.com/paper/2111.11168/) (2021)
- [Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier](https://mlsanity.com/paper/2310.08601/) (2023)
- [Operational risk quantification of power grids using graph neural network surrogates of the DC OPF](https://mlsanity.com/paper/2311.03661/) (2023)
- [A Neural Network Framework for Discovering Closed-form Solutions to Quadratic Programs with Linear Constraints](https://mlsanity.com/paper/2510.23737/) (2025)
- [WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers](https://mlsanity.com/paper/2605.05728/) (2026)

## Abstract (arXiv)

The optimal power flow is an optimization problem used in power systems operational planning to maximize economic efficiency while satisfying demand and maintaining safety margins. Due to uncertainty and variability in renewable energy generation and demand, the optimal solution needs to be updated in response to observed uncertainty realizations or near real-time forecast updates. To address the challenge of computing such frequent real-time updates to the optimal solution, recent literature has proposed the use of machine learning to learn the mapping between the uncertainty realization and the optimal solution. Further, learning the active set of constraints at optimality, as opposed to directly learning the optimal solution, has been shown to significantly simplify the machine learning task, and the learnt model can be used to predict optimal solutions in real-time. In this paper, we propose the use of classification algorithms to learn the mapping between the uncertainty realization and the active set of constraints at optimality, thus further enhancing the computational efficiency of the real-time prediction. We employ neural net classifiers for this task and demonstrate the excellent performance of this approach on a number of systems in the IEEE PES PGLib-OPF benchmark library.