# QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints

arXiv: https://arxiv.org/abs/2401.06820 · HTML: https://mlsanity.com/paper/2401.06820/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 21 of 21)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [End-to-End Learnable Geometric Vision by Backpropagating PnP Optimization](https://mlsanity.com/paper/1909.06043/) (2019)
- [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 Warm-Start Points for AC Optimal Power Flow](https://mlsanity.com/paper/1905.08860/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [Total Variation Optimization Layers for Computer Vision](https://mlsanity.com/paper/2204.03643/) (2022)
- [Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach](https://mlsanity.com/paper/2110.01653/) (2021)
- [A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow](https://mlsanity.com/paper/2110.11991/) (2021)
- [A Two-level ADMM Algorithm for AC OPF with Global Convergence Guarantees](https://mlsanity.com/paper/2008.12139/) (2020)
- [Accelerated Computation and Tracking of AC Optimal Power Flow Solutions using GPUs](https://mlsanity.com/paper/2110.06879/) (2021)
- [Learning Payment-Free Resource Allocation Mechanisms](https://mlsanity.com/paper/2311.10927/) (2023)
- [On Solving Unit Commitment with Alternating Current Optimal Power Flow on GPU](https://mlsanity.com/paper/2310.13145/) (2023)
- [Initializing Successive Linear Programming Solver for ACOPF using Machine Learning](https://mlsanity.com/paper/2007.09210/) (2020)
- [Measurement-Consistent Networks via a Deep Implicit Layer for Solving Inverse Problems](https://mlsanity.com/paper/2211.03177/) (2022)

## Built on by (most cited first, 5 of 5)

- [LUMINA: Foundation Models for Topology Transferable ACOPF](https://mlsanity.com/paper/2603.04300/) (2026)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee](https://mlsanity.com/paper/2512.11127/) (2025)
- [Multi-ResNets for Subspace Preconditioning in Constrained Optimization](https://mlsanity.com/paper/2606.06300/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)

## Abstract (arXiv)

At the heart of power system operations, alternating current optimal power flow (ACOPF) studies the generation of electric power in the most economical way under network-wide load requirement, and can be formulated as a highly structured non-convex quadratically constrained quadratic program (QCQP). Optimization-based solutions to ACOPF (such as ADMM or interior-point method), as the classic approach, require large amount of computation and cannot meet the need to repeatedly solve the problem as load requirement frequently changes. On the other hand, learning-based methods that directly predict the ACOPF solution given the load input incur little computational cost but often generates infeasible solutions (i.e. violate the constraints of ACOPF). In this work, we combine the best of both worlds -- we propose an innovated framework for learning ACOPF, where the input load is mapped to the ACOPF solution through a neural network in a computationally efficient and reliable manner. Key to our innovation is a specific-purpose "activation function" defined implicitly by a QCQP and a novel loss, which enforce constraint satisfaction. We show through numerical simulations that our proposed method achieves superior feasibility rate and generation cost in situations where the existing learning-based approaches fail.