Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE

Hybrid energy supply systems are widely utilized in modern manufacturing processes, where accurately predicting energy consumption is essential not only for managing productivity but also for driving sustainable development. Effective energy management is a cornerstone of sustainable manufacturing, reducing waste and enhancing efficiency. However, conventional studies often focus solely on predicting single types of energy consumption and overlook the integration of physical laws and information, which are essential for a comprehensive understanding of energy dynamics. In this context, this paper introduces a multi-task physics-informed multi-gate mixture-of-experts (pi-MMoE) model that not only considers multiple forms of energy consumption but also incorporates physical principles through the integration of physical information and multi-task modeling. Specifically, a detailed analysis of manufacturing processes and energy patterns is first conducted to study various energy types and extract relevant physical laws. Next, using industry insights and thermodynamic principles, key equations for energy balance and conversion are derived to create a physics-based loss function for model training. Finally, the pi-MMoE model framework is constructed, featuring multi-expert networks and gating mechanisms to balance cross-task knowledge sharing and expert learning. In a case study of a textile factory, the pi-MMoE model reduced electricity and steam prediction errors by 14.28% and 27.27%, respectively, outperforming traditional deep learning methods. This demonstrates that the model can improve prediction performance, providing a novel approach to intelligent energy management and promoting sustainable development in manufacturing.