# Spatial Network Decomposition for Fast and Scalable AC-OPF Learning

arXiv: https://arxiv.org/abs/2101.06768 · HTML: https://mlsanity.com/paper/2101.06768/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 17 Jan 2021.

## Builds on (most cited first, 18 of 18)

- [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)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [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)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [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)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [Learning an Optimally Reduced Formulation of OPF through Meta-optimization](https://mlsanity.com/paper/1911.06784/) (2019)
- [A Learning-boosted Quasi-Newton Method for AC Optimal Power Flow](https://mlsanity.com/paper/2007.06074/) (2020)
- [Hot-Starting the Ac Power Flow with Convolutional Neural Networks](https://mlsanity.com/paper/2004.09342/) (2020)
- [Hybrid Learning Aided Inactive Constraints Filtering Algorithm to Enhance AC OPF Solution Time](https://mlsanity.com/paper/2006.01336/) (2020)
- [Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2007.07002/) (2020)
- [AC-Feasibility on Tree Networks is NP-Hard](https://mlsanity.com/paper/1410.8253/) (2014)
- [An Exact and Scalable Problem Decomposition for Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/1910.03685/) (2019)

## Built on by (most cited first, 15 of 15)

- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [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)
- [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)
- [Risk-Aware Control and Optimization for High-Renewable Power Grids](https://mlsanity.com/paper/2204.00950/) (2022)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Massively Digitized Power Grid: Opportunities and Challenges of Use-inspired AI](https://mlsanity.com/paper/2205.05180/) (2022)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks](https://mlsanity.com/paper/2307.04050/) (2023)
- [Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flow](https://mlsanity.com/paper/2311.18072/) (2023)
- [Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow](https://mlsanity.com/paper/2206.01864/) (2022)
- [Learning-based AC-OPF Solvers on Realistic Network and Realistic Loads](https://mlsanity.com/paper/2205.09452/) (2022)

## Abstract (arXiv)

This paper proposes a novel machine-learning approach for predicting AC-OPF solutions that features a fast and scalable training. It is motivated by the two critical considerations: (1) the fact that topology optimization and the stochasticity induced by renewable energy sources may lead to fundamentally different AC-OPF instances; and (2) the significant training time needed by existing machine-learning approaches for predicting AC-OPF. The proposed approach is a 2-stage methodology that exploits a spatial decomposition of the power network that is viewed as a set of regions. The first stage learns to predict the flows and voltages on the buses and lines coupling the regions, and the second stage trains, in parallel, the machine-learning models for each region. Experimental results on the French transmission system (up to 6,700 buses and 9,000 lines) demonstrate the potential of the approach. Within a short training time, the approach predicts AC-OPF solutions with very high fidelity and minor constraint violations, producing significant improvements over the state-of-the-art. The results also show that the predictions can seed a load flow optimization to return a feasible solution within 0.03% of the AC-OPF objective, while reducing running times significantly.