# Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI

arXiv: https://arxiv.org/abs/2208.08485 · HTML: https://mlsanity.com/paper/2208.08485/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 66 references that are in the map.
- First posted on arXiv 17 Aug 2022.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Streaming Graph Neural Networks via Continual Learning](https://mlsanity.com/paper/2009.10951/) (2020)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Structural Temporal Graph Neural Networks for Anomaly Detection in Dynamic Graphs](https://mlsanity.com/paper/2005.07427/) (2020)
- [TrafficStream: A Streaming Traffic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning](https://mlsanity.com/paper/2106.06273/) (2021)
- [Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks](https://mlsanity.com/paper/1812.09464/) (2018)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networks](https://mlsanity.com/paper/2104.11846/) (2021)
- [Causal Incremental Graph Convolution for Recommender System Retraining](https://mlsanity.com/paper/2108.06889/) (2021)
- [Grid-Graph Signal Processing (Grid-GSP): A Graph Signal Processing Framework for the Power Grid](https://mlsanity.com/paper/2103.06068/) (2021)
- [Physics-Aware Neural Networks for Distribution System State Estimation](https://mlsanity.com/paper/1903.09669/) (2019)
- [FeederGAN: Synthetic Feeder Generation via Deep Graph Adversarial Nets](https://mlsanity.com/paper/2004.01407/) (2020)
- [Spatio-Temporal Graph Convolutional Neural Networks for Physics-Aware Grid Learning Algorithms](https://mlsanity.com/paper/2203.16732/) (2022)

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

- [Detection of False Data Injection Attacks (FDIA) on Power Dynamical Systems With a State Prediction Method](https://mlsanity.com/paper/2409.04609/) (2024)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [Diffusion Maps for Signal Filtering in Graph Learning](https://mlsanity.com/paper/2312.14758/) (2023)
- [Unified Complex-valued Neural Network: A Magnitude-Phase Computational Model for Event-Driven Neuromorphic Learning](https://mlsanity.com/paper/2606.29099/) (2026)

## Abstract (arXiv)

The effective representation, precessing, analysis, and visualization of large-scale structured data over graphs are gaining a lot of attention. So far most of the literature has focused on real-valued signals. However, signals are often sparse in the Fourier domain, and more informative and compact representations for them can be obtained using the complex envelope of their spectral components, as opposed to the original real-valued signals. Motivated by this fact, in this work we generalize graph convolutional neural networks (GCN) to the complex domain, deriving the theory that allows to incorporate a complex-valued graph shift operators (GSO) in the definition of graph filters (GF) and process complex-valued graph signals (GS). The theory developed can handle spatio-temporal complex network processes. We prove that complex-valued GCNs are stable with respect to perturbations of the underlying graph support, the bound of the transfer error and the bound of error propagation through multiply layers. Then we apply complex GCN to power grid state forecasting, power grid cyber-attack detection and localization.