AUTOMATED IDENTIFICATION OF GRAY-BOX MODELS FOR HVAC SYSTEMS - Bueno Uceta,José Antonio (Master's Theses in Mathematical Sciences, 2025)
Today, buildings account for approximately 30% of worldwide energy use, with HVAC (Heating, Ventilation, and Air Conditioning) systems representing nearly 40% of that total. Improving the energy efficiency of HVAC systems is therefore essential for reducing operational costs and mitigating environmental impact. Because HVAC systems operate continuously and under strict operational constraints, accurate models are required to evaluate and optimize different operating strategies. Traditional physics-based models (white-box) are often costly and time-consuming to develop, while purely data-driven models (black-box) tend to lack interpretability and robustness. This thesis investigates whether hybrid approaches, referred to as gray-box models, can offer a more efficient and reliable alternative by integrating both physical knowledge and data. To this end, four modeling strategies are developed and compared: black-box and gray-box models, each implemented with and without a component-based architecture. All models are constructed using Neural Ordinary Differential Equations (NODEs). The goal is to evaluate whether combining physics knowledge with data-driven techniques can reduce the need for large and highly variable training datasets while maintaining or improving model accuracy. The comparison is performed using two key performance metrics: the Relative Root Mean Squared Error (RRMSE) and the Maximum Absolute Error (MAE). Additionally, the complexity required to achieve comparable predictive performance across strategies is analyzed. The results show that, when sufficient training data is available, gray-box models achieve comparable or superior accuracy with fewer parameters than black-box models. Moreover, the inclusion of physical knowledge improves both predictive accuracy and model robustness in scenarios with limited or low-quality training data. Nevertheless, gray-box models still require datasets with sufficient excitation to ensure stable and reliable performance.
Keywords: Gray-box model; Neural Ordinary Differential Equations (NODEs); Physics-informed machine learning; System identification