# Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamics

arXiv: https://arxiv.org/abs/2407.18691 · HTML: https://mlsanity.com/paper/2407.18691/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 26 Jul 2024.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Potential, Challenges and Future Directions for Deep Learning in Prognostics and Health Management Applications](https://mlsanity.com/paper/2005.02144/) (2020)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Graph Neural Networks in IoT: A Survey](https://mlsanity.com/paper/2203.15935/) (2022)
- [Encoder-Decoder Architecture for Supervised Dynamic Graph Learning: A Survey](https://mlsanity.com/paper/2203.10480/) (2022)
- [DyEdgeGAT: Dynamic Edge via Graph Attention for Early Fault Detection in IIoT Systems](https://mlsanity.com/paper/2307.03761/) (2023)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (2024)
- [Physics-Enhanced Graph Neural Networks For Soft Sensing in Industrial Internet of Things](https://mlsanity.com/paper/2404.08061/) (2024)
- [Spatial-Temporal Graph Attention Fuser for Calibration in IoT Air Pollution Monitoring Systems](https://mlsanity.com/paper/2309.04508/) (2023)
- [Virtual Sensor for Real-Time Bearing Load Prediction Using Heterogeneous Temporal Graph Neural Networks](https://mlsanity.com/paper/2404.02304/) (2024)
- [Graph Neural Networks for Electric and Hydraulic Data Fusion to Enhance Short-term Forecasting of Pumped-storage Hydroelectricity](https://mlsanity.com/paper/2404.03368/) (2024)
- [A Two-Stage Bayesian Optimisation for Automatic Tuning of an Unscented Kalman Filter for Vehicle Sideslip Angle Estimation](https://mlsanity.com/paper/2206.15115/) (2022)

## Built on by (most cited first, 7 of 7)

- [Virtual Sensing-Enabled Digital Twin Framework for Real-Time Monitoring of Nuclear Systems Leveraging Deep Neural Operators](https://mlsanity.com/paper/2410.13762/) (2024)
- [Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models](https://mlsanity.com/paper/2509.00639/) (2025)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systems](https://mlsanity.com/paper/2504.13768/) (2025)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Virtual Smart Metering in District Heating Networks via Heterogeneous Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2604.10166/) (2026)
- [Information Density as a Quantitative Measure for AI-enabled Virtual Sensing: Feasibility and Limits](https://mlsanity.com/paper/2605.08180/) (2026)

## Abstract (arXiv)

Real-time condition monitoring is crucial for the reliable and efficient operation of complex systems. However, relying solely on physical sensors can be limited due to their cost, placement constraints, or inability to directly measure certain critical parameters. Virtual sensing addresses these limitations by leveraging readily available sensor data and system knowledge to estimate inaccessible parameters or infer system states. The increasing complexity of industrial systems necessitates deployments of sensors with diverse modalities to provide a comprehensive understanding of system states. These sensors capture data at varying frequencies to monitor both rapid and slowly varying system dynamics, as well as local and global state evolutions of the systems. This leads to heterogeneous temporal dynamics, which, particularly under varying operational end environmental conditions, pose a significant challenge for accurate virtual sensing. To address this, we propose a Heterogeneous Temporal Graph Neural Network (HTGNN) framework. HTGNN explicitly models signals from diverse sensors and integrates operating conditions into the model architecture. We evaluate HTGNN using two newly released datasets: a bearing dataset with diverse load conditions for bearing load prediction and a year-long simulated dataset for predicting bridge live loads. Our results demonstrate that HTGNN significantly outperforms established baseline methods in both tasks, particularly under highly varying operating conditions. These results highlight HTGNN's potential as a robust and accurate virtual sensing approach for complex systems, paving the way for improved monitoring, predictive maintenance, and enhanced system performance. Our code and data are available under https://github.com/EPFL-IMOS/htgnn.