## 4 Discussion
### Metamodels and Data-Driven Models for Energy Forecasting  
There has been a notable transition within the field of architectural design, moving away from conventional problem-solving instruments towards embracing optimisation as a tool for exploration, predominantly in the early design stages [42; 43; 44; 45; 46; 47; 48]. However, the real-world application of optimisation during these early stages remains limited. This limited application can be ascribed to various factors, including the intensive time requirements, difficulties in interpretation, constraints inherent to parametric models, and the frequently indistinct character of performance objectives in the realm of architectural design. Buildings, throughout their lifecycle, contribute to both embodied and operational emissions. While construction primarily results in embodied emissions, operational emissions persist throughout the building's life. These operational emissions are influenced by evolving factors like climate change, electricity grid decarbonisation, and user behaviour. Notably, a discrepancy often exists between a building's design performance and its actual operational performance [49; 50; 51]. This 'performance gap' arises from complex interdependencies not accounted for during optimisation, such as building construction, supply systems, environmental parameters, and occupant behaviour. Considering the influence of global warming on the future performance of buildings, planning based exclusively on historical weather data proves to be inadequate. Therefore, it is of paramount importance to integrate uncertainty into building energy evaluations and meticulously assess the robustness of building energy systems in the face of the forthcoming conditions [50; 52; 53; 54]. Metamodels, also known as data-driven models, act as approximate mathematical depictions crafted to explore the intricate relationships between inputs and outputs that are displayed by more sophisticated physics-based models [55]. Essentially, while mathematical models abstract the real world, data-driven models or metamodels abstract these mathematical models further [56]. Metamodels boast the advantage of being constructible from a modest dataset obtained through the simulation of physics-based models. These models are not only user-friendly but also allow for analytical expression in their formulations. After being adequately trained with a selected set of inputs and outputs from a physics-based model, metamodels possess the capability to forecast outputs for input values that were not part of the initial training set. Conversely, data-driven models, which are trained using data harvested from real buildings, aim to emulate real-world scenarios rather than another model. For a data-driven approach to be effective, extensive long-term measurements across various building types are essential. Nevertheless, this method may predominantly be applicable to existing building stocks, thereby restricting the examination of alternative energy-efficient constructions. In contrast, the metamodelling approach is capable of efficiently producing the necessary database, thereby facilitating the use of virtually unlimited values for design variables. All supervised metamodelling approaches follow a comparable procedure, which includes constructing representative samples of inputs for both training and validation purposes. For each set of inputs, a physics-based model is executed to generate the respective outputs. The metamodel is then trained with the gathered input-output samples utilising a selected technique, followed by a validation process using multiple performance indicators [57; 58; 32]. Upon the completion of these stages, the metamodel is ready for quick deployment in future BPS analyses. Within the sphere of BPS applications, various techniques are prominently utilised, including polynomial regression, multivariate adaptive regression splines (MARS), the Gaussian process (also known as Kriging), SVM, and ANNs. For example, [PERSON] et al.