# Physics-Aware Neural Networks for Distribution System State Estimation

arXiv: https://arxiv.org/abs/1903.09669 · HTML: https://mlsanity.com/paper/1903.09669/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [State and Topology Estimation for Unobservable Distribution Systems using Deep Neural Networks](https://mlsanity.com/paper/2104.07208/) (2021)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
- [Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI](https://mlsanity.com/paper/2208.08485/) (2022)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [Physical Constraint Embedded Neural Networks for inference and noise regulation](https://mlsanity.com/paper/2105.09146/) (2021)
- [Deep Learning-enabled MCMC for Probabilistic State Estimation in District Heating Grids](https://mlsanity.com/paper/2305.15445/) (2023)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [Robust, Deep, and Reinforcement Learning for Management of Communication and Power Networks](https://mlsanity.com/paper/2202.05395/) (2022)
- [Mycelium: A Generalizable Cross-Grid Multi-Task Model for Electrical Distribution Systems](https://mlsanity.com/paper/2609.33120/) (2026)

## Abstract (arXiv)

The distribution system state estimation problem seeks to determine the network state from available measurements. Widely used Gauss-Newton approaches are very sensitive to the initialization and often not suitable for real-time estimation. Learning approaches are very promising for real-time estimation, as they shift the computational burden to an offline training stage. Prior machine learning approaches to power system state estimation have been electrical model-agnostic, in that they did not exploit the topology and physical laws governing the power grid to design the architecture of the learning model. In this paper, we propose a novel learning model that utilizes the structure of the power grid. The proposed neural network architecture reduces the number of coefficients needed to parameterize the mapping from the measurements to the network state by exploiting the separability of the estimation problem. This prevents overfitting and reduces the complexity of the training stage. We also propose a greedy algorithm for phasor measuring units placement that aims at minimizing the complexity of the neural network required for realizing the state estimation mapping. Simulation results show superior performance of the proposed method over the Gauss-Newton approach.