# KCLNet: Physics-Informed Power Flow Prediction via Constraints Projections

arXiv: https://arxiv.org/abs/2506.12902 · HTML: https://mlsanity.com/paper/2506.12902/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 7 of 7)

- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Data-Driven Power Flow Linearization: A Regression Approach](https://mlsanity.com/paper/1710.10621/) (2017)
- [Fast Power system security analysis with Guided Dropout](https://mlsanity.com/paper/1801.09870/) (2018)
- [On the Randomized Kaczmarz Algorithm](https://mlsanity.com/paper/1402.2863/) (2014)
- [Robustness Analysis of AI Models in Critical Energy Systems](https://mlsanity.com/paper/2406.14361/) (2024)

## Built on by (most cited first, 4 of 4)

- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Physics Informed Reinforcement Learning with Gibbs Priors for Topology Control in Power Grids](https://mlsanity.com/paper/2604.01830/) (2026)
- [Test Time Training for AC Power Flow Surrogates via Physics and Operational Constraint Refinement](https://mlsanity.com/paper/2511.22343/) (2025)
- [Differentiable Power-Flow Optimization](https://mlsanity.com/paper/2603.28203/) (2026)

## Abstract (arXiv)

In the modern context of power systems, rapid, scalable, and physically plausible power flow predictions are essential for ensuring the grid's safe and efficient operation. While traditional numerical methods have proven robust, they require extensive computation to maintain physical fidelity under dynamic or contingency conditions. In contrast, recent advancements in artificial intelligence (AI) have significantly improved computational speed; however, they often fail to enforce fundamental physical laws during real-world contingencies, resulting in physically implausible predictions. In this work, we introduce KCLNet, a physics-informed graph neural network that incorporates Kirchhoff's Current Law as a hard constraint via hyperplane projections. KCLNet attains competitive prediction accuracy while ensuring zero KCL violations, thereby delivering reliable and physically consistent power flow predictions critical to secure the operation of modern smart grids.