Virtual Smart Metering in District Heating Networks via Heterogeneous Spatial-Temporal Graph Neural Networks

2026-04-11

AI Summary

This study addresses the limited observability of district heating networks caused by sparse and faulty sensor deployments, which hinders intelligent operation. To overcome this challenge, the authors propose a virtual smart heat metering approach based on a heterogeneous spatio-temporal graph neural network (HSTGNN)—the first application of HSTGNN to virtual metering in district heating systems. The method jointly models cross-variable and spatio-temporal dependencies among pressure, flow rate, and temperature, integrating physical constraints with data-driven learning. Concurrently, the work introduces and publicly releases the first high-resolution, laboratory-scale, synchronously sensed dataset for district heating. Experimental results demonstrate that the proposed approach significantly outperforms existing baselines under real-world operating conditions, substantially improving virtual metering accuracy and system-wide monitoring capabilities.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Application Domains: Internet of Things, Sensor Networks & Smart Cities

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Social Networks and Social Media: Computational social science

Abstract

Intelligent operation of thermal energy networks aims to improve energy efficiency, reliability, and operational flexibility through data-driven control, predictive optimization, and early fault detection. Achieving these goals relies on sufficient observability, requiring continuous and well-distributed monitoring of thermal and hydraulic states. However, district heating systems are typically sparsely instrumented and frequently affected by sensor faults, limiting monitoring. Virtual sensing offers a cost-effective means to enhance observability, yet its development and validation remain limited in practice. Existing data-driven methods generally assume dense synchronized data, while analytical models rely on simplified hydraulic and thermal assumptions that may not adequately capture the behavior of heterogeneous network topologies. Consequently, modeling the coupled nonlinear dependencies between pressure, flow, and temperature under realistic operating conditions remains challenging. In addition, the lack of publicly available benchmark datasets hinders systematic comparison of virtual sensing approaches. To address these challenges, we propose a heterogeneous spatial-temporal graph neural network (HSTGNN) for constructing virtual smart heat meters. The model incorporates the functional relationships inherent in district heating networks and employs dedicated branches to learn graph structures and temporal dynamics for flow, temperature, and pressure measurements, thereby enabling the joint modeling of cross-variable and spatial correlations. To support further research, we introduce a controlled laboratory dataset collected at the Aalborg Smart Water Infrastructure Laboratory, providing synchronized high-resolution measurements representative of real operating conditions. Extensive experiments demonstrate that the proposed approach significantly outperforms existing baselines.

Problem

• virtual sensing
• district heating networks
• observability
• heterogeneous network topologies
• spatial-temporal dependencies

Innovation

• heterogeneous spatial-temporal graph neural network
• virtual smart metering
• district heating networks
• coupled nonlinear dependencies
• benchmark dataset