Development and evaluation of cooling tower performance prediction using physics-informed neural networks

Accurate prediction of outlet water temperature in cooling towers is crucial for implementing energy-efficient control strategies in air-conditioning systems, ultimately leading to reduced energy consumption in building operations. This study investigates the application of physics-informed neural networks (PINN) to leverage the strengths of both physical and data-driven models for predicting cooling tower performance. To achieve this, four experiments were conducted, resulting in the training of 2700 PINN models and 1900 artificial neural network (ANN) models. The predictive performance of the PINN models, developed through various methodologies, was thoroughly evaluated. The findings revealed that incorporating physical constraints into ANN models to form PINN models significantly decreased prediction errors and reduced model training costs. Based on the experimental results, this study proposes a systematic approach for constructing PINN models for cooling tower performance prediction. Key recommendations include: setting the proportion of physical constraints to 0.1, utilizing training data that constitutes 20 % of the dataset in both quantity and domain length, and ensuring that the distribution of the training data is centered within the prediction dataset. In the case analysis, the mean relative error (MRE) and root mean square error (RMSE) of the PINN model developed using the suggested methodology were 2.070 % and 0.309 °C, respectively. In comparison to the ANN model, the MRE improved by 4.712 %, and the RMSE decreased by 0.626 °C. These results demonstrate that PINN models offer significant advantages and considerable potential for predicting cooling tower performance, especially in scenarios with limited training data and narrowly distributed datasets.