PINN-GNN Hybrid Neural Networks for Precise PUE Prediction in Data Centers

Accurate energy efficiency prediction is fundamental to green computing and low-carbon 6G infrastructure. Data centers represent a challenging testbed due to their high energy density and complex device interactions. Existing methods either ignore physical laws or fail to capture spatial dependencies among heterogeneous devices. To address these limitations, this paper proposes a hybrid framework integrating Physics-Informed Neural Networks (PINNs) with Graph Neural Networks (GNNs) for Power Usage Effectiveness (PUE) prediction. Two algorithmic variants are developed: Physically Decomposed PINN-GNN (PDPG) and Unified End-to-End PINN-GNN (UEPG). Physical regularization constraints derived from practical energy and thermal principles are embedded into model training to improve the physical rationality of the prediction results. Validated on real-world data center datasets, the proposed method achieves superior accuracy and robustness over mainstream baselines, providing reliable support for cooling and resource management.