# Compact Optimization Learning for AC Optimal Power Flow

arXiv: https://arxiv.org/abs/2301.08840 · HTML: https://mlsanity.com/paper/2301.08840/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 21 Jan 2023.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [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)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems](https://mlsanity.com/paper/1902.01697/) (2019)
- [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)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation](https://mlsanity.com/paper/2008.11827/) (2020)
- [Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach](https://mlsanity.com/paper/2006.00544/) (2020)
- [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)
- [Data-Driven Time Series Reconstruction for Modern Power Systems Research](https://mlsanity.com/paper/2110.13772/) (2021)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Feasibility Layer Aided Machine Learning Approach for Day-Ahead Operations](https://mlsanity.com/paper/2208.06742/) (2022)
- [Optimization-Based Bound Tightening using a Strengthened QC-Relaxation of the Optimal Power Flow Problem](https://mlsanity.com/paper/1809.04565/) (2018)
- [Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility](https://mlsanity.com/paper/1902.04815/) (2019)
- [Benchmarking Large-Scale ACOPF Solutions and Optimality Bounds](https://mlsanity.com/paper/2203.11328/) (2022)
- [Restoring AC Power Flow Feasibility from Relaxed and Approximated Optimal Power Flow Models](https://mlsanity.com/paper/2209.04399/) (2022)

## Built on by (most cited first, 11 of 11)

- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [AI4OPT: AI Institute for Advances in Optimization](https://mlsanity.com/paper/2307.02671/) (2023)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flow](https://mlsanity.com/paper/2311.18072/) (2023)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [DiffOPF: Diffusion Solver for Optimal Power Flow](https://mlsanity.com/paper/2510.14075/) (2025)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatch](https://mlsanity.com/paper/2510.15850/) (2025)
- [Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow](https://mlsanity.com/paper/2511.11677/) (2025)

## Abstract (arXiv)

This paper reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This paper first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes Compact Learning, a new method that learns in a subspace of the principal components before translating the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. Compact Learning is evaluated on a variety of test cases from the PGLib with up to 30,000 buses. The paper also shows that the output of Compact Learning can be used to warm-start an exact AC solver to restore feasibility, while bringing significant speed-ups.