# A Graph Neural Network with Auxiliary Task Learning for Missing PMU Data Reconstruction

arXiv: https://arxiv.org/abs/2512.24542 · HTML: https://mlsanity.com/paper/2512.24542/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 31 Dec 2025.

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

- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [ForkMerge: Mitigating Negative Transfer in Auxiliary-Task Learning](https://mlsanity.com/paper/2301.12618/) (2023)
- [Real-time Faulted Line Localization and PMU Placement in Power Systems through Convolutional Neural Networks](https://mlsanity.com/paper/1810.05247/) (2018)
- [Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning](https://mlsanity.com/paper/1811.02756/) (2018)
- [Physics-informed Graphical Neural Network for Power System State Estimation](https://mlsanity.com/paper/2312.17738/) (2023)
- [Topology and Admittance Estimation: Precision Limits and Algorithms](https://mlsanity.com/paper/2106.00532/) (2021)
- [Topology-Aware Graph Neural Network-based State Estimation for PMU-Unobservable Power Systems](https://mlsanity.com/paper/2506.03493/) (2025)
- [Robust Recovery of Missing Data in Electricity Distribution Systems](https://mlsanity.com/paper/1708.01583/) (2017)
- [Decentralized Low-Rank State Estimation for Power Distribution Systems](https://mlsanity.com/paper/1910.04831/) (2019)
- [A Model-Agnostic Method for PMU Data Recovery Using Optimal Singular Value Thresholding](https://mlsanity.com/paper/2108.03220/) (2021)

## Abstract (arXiv)

In wide-area measurement systems (WAMS), phasor measurement unit (PMU) measurement is prone to data missingness due to hardware failures, communication delays, and cyber-attacks. Existing data-driven methods are limited by inadaptability to concept drift in power systems, poor robustness under high missing rates, and reliance on the unrealistic assumption of full system observability. Thus, this paper proposes an auxiliary task learning (ATL) method for reconstructing missing PMU data. First, a K-hop graph neural network (GNN) is proposed to enable direct learning on the subgraph consisting of PMU nodes, overcoming the limitation of the incompletely observable system. Then, an auxiliary learning framework consisting of two complementary graph networks is designed for accurate reconstruction: a spatial-temporal GNN extracts spatial-temporal dependencies from PMU data to reconstruct missing values, and another auxiliary GNN utilizes the low-rank property of PMU data to achieve unsupervised online learning. In this way, the low-rank properties of the PMU data are dynamically leveraged across the architecture to ensure robustness and self-adaptation. Numerical results demonstrate the superior offline and online performance of the proposed method under high missing rates and incomplete observability.