# Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow

arXiv: https://arxiv.org/abs/2410.04818 · HTML: https://mlsanity.com/paper/2410.04818/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [Solutions of DC OPF are Never AC Feasible](https://mlsanity.com/paper/1912.00319/) (2019)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Convex Relaxation of Optimal Power Flow, Part II: Exactness](https://mlsanity.com/paper/1405.0814/) (2014)
- [Learning the Optimal Power Flow: Environment Design Matters](https://mlsanity.com/paper/2403.17831/) (2024)
- [Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach](https://mlsanity.com/paper/2110.01653/) (2021)
- [Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem](https://mlsanity.com/paper/2007.05334/) (2020)
- [Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality](https://mlsanity.com/paper/2212.03977/) (2022)
- [Presolving Convexified Optimal Power Flow with Mixtures of Gradient Experts](https://mlsanity.com/paper/2312.07276/) (2023)

## Built on by (most cited first, 1 of 1)

- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)

## Abstract (arXiv)

We present PINCO, an unsupervised learning framework that integrates Graph Neural Networks with physics-informed neural networks for AC optimal power flow (AC-OPF) solutions. Unlike state-of-the-art unsupervised methods that require prescreened datasets containing only feasible instances, our approach operates on unfiltered data, including ill-conditioned cases. The framework addresses two critical gaps in the literature: (1) robustness to topology changes up to N-2 contingencies, and (2) detecting optimal power flow instances that are infeasible without relying on traditional solvers for data filtering. PINCO embeds physical laws into the learning process via augmented Lagrangian multipliers. In addition, it introduces a clustering branch with learnable centroids that automatically separate feasible from infeasible solutions based on constraint-violation patterns. We evaluate the framework across systems of varying complexity, including the IEEE 30-bus, IEEE 57-bus, and Swiss transmission networks, demonstrating scalability and robustness under diverse loading conditions and topology variations. Benchmarking against DeepOPF-FT and the IPOPT solver shows that PINCO achieves comparable constraint satisfaction while delivering two to three orders of magnitude computational speedup compared to IPOPT and lower operational costs across all configurations.