## 1 Introduction  
With the growing needs of emerging economies, global building stock is projected to increase by more than 230 billion square meters by 2060, with over 50% growth in building energy demand [1]. Therefore, reducing carbon emissions in the residential building sector holds enormous potential for decarbonization and achieving the global 1.5 \({}^{\circ}\)C target [2]. Renovating existing buildings could decrease the total energy consumption of the European Union (EU) by 5-6% and lower CO\({}_{2}\) emissions by around 5% [3]. Approximately 60-70% of the total energy consumption of residential buildings, about 180 kWh/m\({}^{2}\)[4], is due to space heating and cooling [5]. This high consumption is often due to the poor thermos physical properties of the building envelope, characterized by high thermal transmittance and low thermal inertia [6]. One of the main goals of the EU \"Green Deal\" policy is the reduction in the primary energy demand for space heating systems [7]. In this context, the \"Fit for 55\" package aims to cut CO\({}_{2}\) emissions by 55% relative to 1990 levels by 2030. Consequently, energy actions based on the adoption of thermal insulation materials for building external walls are very common [8]. Another key energy measure involves replacing inefficient gas-fired boilers, which typically have a thermal efficiency ranging from 75% to 85%, with modern condensing boilers. These boilers achieve thermal efficiencies greater than 100% by utilizing both sensible and latent heat through the condensation of exhaust gases [9]. Additionally, the Energy Performance of Buildings Directive (EPBD) of March 2023 emphasizes the need for green buildings to meet stringent energy performance standards. This directive mandates significant improvements in building energy efficiency to align with the EU climate targets. Various incentives and funding mechanisms are available to support these upgrades, ensuring compliance with the EPBD requirements and promoting widespread adoption of energy-efficient practices [3]. In Italy, the Superbonus 110% is one of the most significant incentives for building retrofit projects. This program allows homeowners to deduct 110% of the costs for energy efficiency improvements, including insulation, heating system replacements, and the installation of solar panels. The Superbonus stands out because it covers not only the full cost of the interventions but also the related expenses, such as feasibility studies and technical reports, effectively making the upgrades cost-free for the beneficiaries. This incentive has been instrumental in accelerating the adoption of energy-saving measures across Italy, promoting energy-efficient practices at a large scale. Due to its generous nature and comprehensive coverage, it is widely regarded as the most effective incentive for achieving the nation's energy efficiency targets [10]. Other incentives exist, such as Ecolonus and Sismabonus, but the Superbonus 110% is unparalleled in its impact and scope [11]. Energy renovation of the residential building envelope can notably reduce the building's primary energy demand for space heating and cooling [12]. It should be noted that the EU sets the directives and overall framework for energy efficiency improvements, while the implementation and provision of incentives are managed by individual member states. National governments are responsible for developing specific measures and funding programs to meet the EU targets within their own contexts. As a result, EU Countries have increasingly provided public incentives to improve building stock renovation. An interesting review of EU energy efficiency policies for buildings is presented in ref. [13]. Several techniques to enhance the energy performance of buildings are documented in the literature [14; 15].