# Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning

arXiv: https://arxiv.org/abs/1811.02756 · HTML: https://mlsanity.com/paper/1811.02756/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

## Built on by (most cited first, 14 of 14)

- [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)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
- [Robust Power System State Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.05874/) (2025)
- [Deep Learning for Intelligent Demand Response and Smart Grids: A Comprehensive Survey](https://mlsanity.com/paper/2101.08013/) (2021)
- [Power System Anomaly Detection and Classification Utilizing WLS-EKF State Estimation and Machine Learning](https://mlsanity.com/paper/2209.12629/) (2022)
- [Deep Learning-enabled MCMC for Probabilistic State Estimation in District Heating Grids](https://mlsanity.com/paper/2305.15445/) (2023)
- [Analytical Verification of Performance of Deep Neural Network Based Time-Synchronized Distribution System State Estimation](https://mlsanity.com/paper/2311.06973/) (2023)
- [Robust Deep Reinforcement Learning for Inverter-based Volt-Var Control in Partially Observable Distribution Networks](https://mlsanity.com/paper/2408.06776/) (2024)
- [Time-Synchronized Full System State Estimation Considering Practical Implementation Challenges](https://mlsanity.com/paper/2212.01729/) (2022)
- [Creating Temporally Correlated High-Resolution Profiles of Load Injection Using Constrained Generative Adversarial Networks](https://mlsanity.com/paper/2311.12166/) (2023)
- [Physics-Constrained Neural Dynamics: A Unified Manifold Framework for Large-Scale Power Flow Computation](https://mlsanity.com/paper/2512.01207/) (2025)
- [Neural Network Optimal Power Flow via Energy Gradient Flow and Unified Dynamics](https://mlsanity.com/paper/2512.01219/) (2025)
- [A Graph Neural Network with Auxiliary Task Learning for Missing PMU Data Reconstruction](https://mlsanity.com/paper/2512.24542/) (2025)

## Abstract (arXiv)

The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors and the presence of bad and missing data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation via deep learning neural network outperforms existing benchmarks.