# Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow

arXiv: https://arxiv.org/abs/2511.11677 · HTML: https://mlsanity.com/paper/2511.11677/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 11 Nov 2025.

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

- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Deep Declarative Networks: A New Hope](https://mlsanity.com/paper/1909.04866/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach](https://mlsanity.com/paper/1906.06017/) (2019)
- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach](https://mlsanity.com/paper/2110.01653/) (2021)
- [Incremental Model Building Homotopy Approach for Solving Exact AC-Constrained Optimal Power Flow](https://mlsanity.com/paper/2011.00587/) (2020)
- [Robust Convergence of Power Flow using Tx Stepping Method with Equivalent Circuit Formulation](https://mlsanity.com/paper/1711.01471/) (2017)
- [Robust and Efficient Power Flow Convergence with G-min Stepping Homotopy Method](https://mlsanity.com/paper/1904.04932/) (2019)

## Abstract (arXiv)

Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a textithomotopy-guided self-supervised L2O method for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.