AUTOMATED IDENTIFICATION OF GRAY-BOX MODELS FOR HVAC SYSTEMS

Abstract

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.

Popular Abstract

Imagine walking into a building on a hot summer day and feeling a refreshing cool breeze. Most people do not think much about what is happening behind the scenes, but there is a complex system of machines that work continuously to keep the indoor environment comfortable. These are known as HVAC (Heating, Ventilation, and Air Conditioning) systems, and they are used not only for human comfort, but also for industrial purposes such as cooling data centers. Nowadays, HVAC systems account for approximately 10% of the energy consumption in buildings across the globe. Therefore, improving their efficiency can lead to substantial savings in both energy and cost.
Traditionally, engineers have modeled HVAC systems using a “white-box” approach, which relies on physical laws such as thermodynamics and fluid dynamics. These models can be very accurate, but often require significant time and expert knowledge. In the past years, a new approach known as “black-box” uses machine learning techniques to find patterns in data without considering the underlying physics. While easier to construct, black-box models usually yield unreliable predictions outside the range of the data they have been trained on.
In this work, a third alternative is explored, the “gray-box” model, which aims to combine the strengths of both white-box and black-box methods. For this, it uses data from real or simulated systems while also incorporating basic physical knowledge to guide the learning process. The key method used in this thesis is called Neural Ordinary Differential Equations, or NODEs.
Such a model can be used to explore how changes in the operation of individual components influence the system’s performance. Therefore, it is possible to identify configurations that reduce energy consumption without performing lengthy or risky experiments on the actual equipment. This is particularly valuable in environments like data centers, where stability and reliability are crucial.

• author: Bueno Uceta, José Antonio
• supervisor: Philipp Birken; Viktor Linders
• organization: Mathematics (Faculty of Sciences); Centre for Mathematical Sciences
• course: BERM03 20251
• year: 2025
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: Gray-box model, Neural Ordinary Differential Equations (NODEs), Physics-informed machine learning, System identification
• publication/series: Master's Theses in Mathematical Sciences
• report number: LUNFBV-3002-2025
• ISSN: 1404-6342
• other publication id: 2025:E49
• language: English
• id: 9204951
• date added to LUP: 2025-06-26 13:58:21
• date last changed: 2025-06-26 13:58:21