# A Hybrid GNN-LSE Method for Fast, Robust, and Physically-Consistent AC Power Flow

arXiv: https://arxiv.org/abs/2510.22020 · HTML: https://mlsanity.com/paper/2510.22020/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow with Continual Learning](https://mlsanity.com/paper/2603.16879/) (2026)
- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)

## Abstract (arXiv)

Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a Physics-Informed Graph Neural Network (GNN) with a robust, iterative Linear State Estimation (LSE) refinement step to produce fast and physically-consistent solutions. The GNN, trained with a physics-informed loss function featuring an efficient dynamic weighting scheme, rapidly predicts a high-quality initial system state. This prediction is then refined using an iterative, direct linear solver inspired by state estimation techniques. This LSE refinement step solves a series of linear equations to enforce physical laws, effectively bypassing the non-linearities and convergence issues of traditional solvers. The proposed GNN-LSE framework is comprehensively validated on systems ranging from small radial distribution networks (IEEE 33-bus, 69-bus) to a large, meshed transmission system (IEEE 118-bus). Results show that our GNN variants are up to 8.4 × 103 times faster than NR. The LSE refinement provides a fast route to a physically-consistent solution, while heavy-loading stress tests (120%-150% of nominal) and N-1 contingencies demonstrate the method's reliability and generalization. This work presents a powerful and flexible framework for bridging fast, data-driven models with the rigorous constraints of power system physics, offering a practical tool for real-time operations and analysis.