# Unified Heterogeneous Graph Neural Network solver for Power Flow, Optimal Power Flow and State Estimation

arXiv: https://arxiv.org/abs/2609.16738 · HTML: https://mlsanity.com/paper/2609.16738/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Learning to run a power network challenge for training topology controllers](https://mlsanity.com/paper/1912.04211/) (2019)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [State Estimation in Electric Power Systems Leveraging Graph Neural Networks](https://mlsanity.com/paper/2201.04056/) (2022)
- [Neural Network-based Power Flow Model](https://mlsanity.com/paper/2112.08418/) (2021)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Enhancing Power Flow Estimation with Topology-Aware Gated Graph Neural Networks](https://mlsanity.com/paper/2507.02078/) (2025)

## Abstract (arXiv)

Power Flow (PF), Optimal Power Flow (OPF), and State Estimation (SE) are fundamental problems in power system analysis, but solving them is computationally expensive. Graph Neural Networks (GNNs) have been proposed as fast surrogates, yet existing solvers are trained for a single problem at a time, producing narrow models that must be rebuilt for each new task. We propose a more general approach: a single Heterogeneous Residual Gated Graph Convolutional Network that solves all three problems with one shared backbone. Rather than learning one mapping, the model learns a reusable representation of how the network behaves, from which PF, OPF, and SE can each be estimated. Trained jointly on the three problems across diverse topologies and loading conditions, and evaluated on the IEEE 14-bus and 118-bus systems, the shared model matches the accuracy of task-specific GNN solvers and stays robust on unseen loading levels and topologies. These results show that a single model can capture the basic operation of a power network and serve several analysis tasks at once, a first step toward a foundation model for power systems.