# Heat Loss Coefficient Estimation Applied to Existing Buildings through Machine Learning Models
## 1 Introduction  
Energy efficiency in buildings is a key roadmap to achieve sustainable development worldwide. Nearly one third of the primary energy consumed in the world comes from non-industrial buildings, and it is similar to all the energy used in the transport sector [1]. Consequently, the residential sector constitutes the largest contributor to global warming by means of carbon dioxide emissions. To achieve the goal of reducing building energy consumption, international cooperation is crucial. The European Union (EU) has created a strict legislative framework implementing two important directives: Energy Performance of Buildings Directive 2010/31/EU (EPBD) [2] and the Energy Efficiency Directive 2012/27/EU [3]. Both of them were updated and amended over the years. Specifically, the Directive amending the Energy Performance of Buildings Directive 2018/844/EU [4] includes different aspects strengthening thecommitment of real building stock modernisation through technological improvements [5]. On the other hand, the International Energy Agency (IEA) is also working hard on this issue by means of its Energy in Buildings and Community (EBC) research programme developing activities towards Nearly Zero Energy Buildings (NZEB), the reduction of carbon dioxide emissions and energy savings technologies. One of the high priority research project themes is the building envelope. The envelope of a building is one of the main sources of heat transfer between the exterior and the interior of the rooms, and it is responsible for the difference between the conditions predicted at the design stage and the actual conditions of the use of the building, including lighting, occupancy and Heating, Ventilation and Air Conditioning (HVAC) systems' operation. This is called the performance gap between building design and operation [6; 7]. The envelope efficiency of a building can be characterized under in-use conditions by calculating the Heat Loss Coefficient (HLC) [8]. This coefficient determines the rate of heat flow through the buildings' envelope when a temperature difference exists between the indoor air and the outdoor air under steady state conditions [9]. Therefore, the accurate estimation of the HLC contributes to optimizing the energy consumption of a building. On the other hand, building energy performance simulation tools have been used in recent years to analyse the energy behaviour of buildings [10]. However, achieving an accurate simulation is not trivial. Many sources of error are introduced into the simulation: occupancy and user's behaviour, weather data [11], envelope materials and thickness, the use of electric equipment, etc. The alternative to simulation is the monitoring of the building operation, which leads to the difficulty of the installation of sensors in in-use buildings. Therefore, in this context, the application of advanced mathematical modelling techniques, such as machine learning methods, is becoming more and more common [12]. There are three widely used building energy prediction models: the white-box (physics-based), black-box (data-driven) and grey-box (a combination of physics based and data-driven) modelling approaches [13]. The application of black-box models in building energy analysis has been consolidated in recent years. These models have received considerable attention because of their great success in learning complex patterns and being able to make accurate predictions without specific knowledge of the subject [14; 15]. Machine Learning (ML) models, also known as black-box models, are specific mathematical models that are capable of learning a pattern from data and extrapolating it to a new sample. Thus, they were widely applied in studies presenting control strategies to reduce energy costs. Three of the most used are: eXtreme Gradient Boosting (XGBoost), Support Vector Regression (SVR) and Multi-Layer Perceptron (MLP) neural network.