# Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow

arXiv: https://arxiv.org/abs/2610.05959 · HTML: https://mlsanity.com/paper/2610.05959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 5 Oct 2026.

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

- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [LUMINA: Foundation Models for Topology Transferable ACOPF](https://mlsanity.com/paper/2603.04300/) (2026)
- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [Improving Feasibility via Fast Autoencoder-Based Projections](https://mlsanity.com/paper/2604.03489/) (2026)
- [Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator](https://mlsanity.com/paper/2509.22458/) (2025)
- [A Hybrid GNN-LSE Method for Fast, Robust, and Physically-Consistent AC Power Flow](https://mlsanity.com/paper/2510.22020/) (2025)
- [Accelerated Probabilistic Power Flow in Electrical Distribution Networks via Model Order Reduction and Neumann Series Expansion](https://mlsanity.com/paper/2010.14995/) (2020)
- [Parameter-Efficient Domain Adaptation of Physics-Informed Self-Attention based GNNs for AC Power Flow Prediction](https://mlsanity.com/paper/2602.18227/) (2026)
- [Newton's Lantern: A Reinforcement Learning Framework for Finetuning AC Power Flow Warm Start Models](https://mlsanity.com/paper/2605.11102/) (2026)

## Abstract (arXiv)

Recent neural power-flow solvers, including emerging foundation models, achieve accurate voltage predictions, yet such accuracy does not necessarily imply physically consistent solutions. Even small complex voltage errors can yield large AC power-balance residuals. We study this accuracy-consistency gap across PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA on realistic 2224-bus Great Britain network (GBnetwork) scenarios, with cross-grid evaluation of GridSFM over 31 systems. Using a singular value decomposition (SVD) basis fitted to training AC power-flow solutions, we find that neural prediction errors contain substantial components outside the dominant solution subspace. To address this mismatch, calibrated solution-subspace projection (CSP) suppresses off-subspace prediction components after train-only bias calibration, reducing Mean PB by 67.0%, 37.8%, 40.5%, and 68.9% for PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA, respectively, relative to calibrated predictions, while improving voltage-magnitude accuracy in all four models. These results identify output-error geometry as an important factor in physics-consistent neural AC power flow. Code: https://github.com/Kimchangheon/neural-acpf-error-geometry