# Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator

arXiv: https://arxiv.org/abs/2509.22458 · HTML: https://mlsanity.com/paper/2509.22458/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [Known Operator Learning and Hybrid Machine Learning in Medical Imaging -- A Review of the Past, the Present, and the Future](https://mlsanity.com/paper/2108.04543/) (2021)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Physics-Guided Graph Neural Networks for Real-time AC/DC Power Flow Analysis](https://mlsanity.com/paper/2305.00216/) (2023)
- [Data driven approach towards more efficient Newton-Raphson power flow calculation for distribution grids](https://mlsanity.com/paper/2504.11650/) (2025)
- [Multi-fidelity power flow solver](https://mlsanity.com/paper/2205.13362/) (2022)

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

- [Parameter-Efficient Domain Adaptation of Physics-Informed Self-Attention based GNNs for AC Power Flow Prediction](https://mlsanity.com/paper/2602.18227/) (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)

Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace the classic NewtonRaphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the soft constraint on the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases to form a fully differentiable knownoperator layer inside the computation graph, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4-32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08 deg in angle, outperforming the PIGNN-MLP baseline by 99.5% and 87.1%, respectively. With streaming micro-batches, it delivers 2-5x faster batched inference than NR on 4-1024-bus grids.