# Knowledge-Assisted Multi-Graph Dependency Learning for Multivariate Time Series Anomaly Detection in Multi-Stage Industrial Processes

arXiv: https://arxiv.org/abs/2607.15799 · HTML: https://mlsanity.com/paper/2607.15799/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 57 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Deep Learning for Time Series Anomaly Detection: A Survey](https://mlsanity.com/paper/2211.05244/) (2022)
- [Learning Graph Structures with Transformer for Multivariate Time Series Anomaly Detection in IoT](https://mlsanity.com/paper/2104.03466/) (2021)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [MST-GAT: A Multimodal Spatial-Temporal Graph Attention Network for Time Series Anomaly Detection](https://mlsanity.com/paper/2310.11169/) (2023)
- [CARLA: Self-supervised Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2308.09296/) (2023)
- [Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis](https://mlsanity.com/paper/2408.13082/) (2024)
- [Entropy Causal Graphs for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.09478/) (2023)
- [Causality-Aware Contrastive Learning for Robust Multivariate Time-Series Anomaly Detection](https://mlsanity.com/paper/2506.03964/) (2025)
- [Spacecraft Anomaly Detection with Attention Temporal Convolution Network](https://mlsanity.com/paper/2303.06879/) (2023)
- [Edge Conditional Node Update Graph Neural Network for Multi-variate Time Series Anomaly Detection](https://mlsanity.com/paper/2401.13872/) (2024)
- [Order-based Causal Discovery for Multistage Processes](https://mlsanity.com/paper/2607.03971/) (2026)

## Built on by (most cited first, 1 of 1)

- [GT-PSSM: Unified Probabilistic Framework for Stochastic Dynamics Modeling and Dependency Learning in Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.34161/) (2026)

## Abstract (arXiv)

Industrial processes often generate complex, interdependent time-series data from multiple sensors across multiple stages, forming complex dependencies among variables and process stages. Effective monitoring and timely anomaly detection of these time series through multivariate time series anomaly detection (MTAD) is crucial for preventing failures and ensuring the reliability of automated systems. Graph neural networks (GNNs) have advanced MTAD by leveraging data-driven graphs to model complex dependencies among variables, effectively capturing relational structures within multivariate time series to enhance anomaly detection performance. However, existing GNN-based approaches often overlook critical process knowledge, and even when this knowledge is considered, seamlessly incorporating it into existing models remains inherently challenging, leading to suboptimal performance. To address this limitation, we propose a knowledge-assisted multi-graph framework for modeling sensor dependencies in multi-stage industrial processes for MTAD, which explicitly incorporates process knowledge into graph learning to enhance dependency modeling and improve anomaly detection performance. Our method constructs three complementary graphs: one purely data-driven and two refined by integrating structural constraints derived from process knowledge. To effectively leverage these graphs for anomaly detection, we employ a multi-graph attention network, enabling a more accurate and robust representation of complex dependencies. Comprehensive experiments on two real-world, multi-stage industrial datasets demonstrate that incorporating process knowledge substantially enhances anomaly detection performance.