Volume 65

Physics-Informed Graph Neural Networks (PIGNN) for Flowrates Forecasting in District Heating Networks Alejandro Martin-Gil, Femke Janssen, Jonah Poort

Abstract

District heating networks require fast and accurate forecasting tools, but classical numerical models are too slow for real-time use, and standard machine learning approaches cannot adapt to changing topologies. In addition, purely data-driven methods fail to take into account physical phenomena, such as mass conservation. Therefore, we propose a Physics-Informed Graph Neural Network (PIGNN) that incorporates the continuity equation into the loss function to enhance accuracy and convergence. Trained on ca. 32,000 samples from 620 hypothetical topologies, the PIGNN achieves a Pearson correlation coefficient of 0.91 (vs. 0.76 for a baseline GNN), converges faster, and provides a computational speedup of 4–5 orders of magnitude over classical methods. This makes it a promising tool for design exploration and operational planning in district heating networks.

Keywords Graph Neural Network, District Heating Networks, Artificial Intelligence, Forecasting, Semi-Supervised Learning.