Adaptive physically consistent neural networks for data center thermal dynamics modeling

Data centers (DCs) are vital for large-scale Internet services, yet their energy consumption poses a significant concern. Energy modeling for DCs is crucial for design, control, and retrofitting. Traditional physic-based models lack flexibility, while Neural Networks (NN) may not strictly adhere to physical principles and demand extensive data. The Physically Consistent Neural Networks (PCNN) framework, which incorporates physical laws into NN through positive coefficients, is introduced. Despite its innovative approach, PCNN struggles with accuracy and generalization in real-world thermal environments due to its reliance on empirically predetermined, static coefficients, which are costly to derive and limit adaptability to dynamic conditions. To address these limitations, this study proposes the Adaptive Physically Consistent Neural Networks (A-PCNN) framework. A-PCNN leverages NN with Softplus activation functions, replacing traditional preset and fixed coefficients to reduce trial-and-error costs and increase flexibility. Over a six-month real data center dataset case study, the A-PCNN framework significantly outperformed the traditional PCNN model. Specifically, it reduced the Mean Absolute Error by 17.3 % for a 15-min forecast and by 79.2 % over a seven-day period, using a Multilayer Perceptron (MLP) as the base model. Furthermore, the A-PCNN framework demonstrates remarkable adaptability. Whether based on a MLP or Long Short-Term Memory (LSTM) model, it consistently surpasses traditional methods in predictive accuracy across time frames from 15 min to 7 days. Its superior performance is especially notable in longer forecast periods.