## 1 Introduction  
The adoption of QSPR/QSAR (Quantitative Structure Property/Activity Relationship) models has become very widespread for the prediction of various properties (e.g., physico-chemical, environmental, toxicological, safety-related) or activities (e.g., biological, pharmacological) on the basis of molecular structure. Being trained with a defined database of molecules, the applicability of these models to a new molecule is, however, limited to the so-called \"applicability domain\" (AD), i.e., the chemical structure and response space within which a model can make predictions with a given reliability [1]. The chemical structure refers to the structural and physico-chemical information that is provided by the descriptors, while the response corresponds to the predicted property or activity, namely the enthalpy of formation or the entropy, in the present study. This AD is crucial, as the final goal of QSPR/QSAR models is to be able to apply them for the prediction of the target endpoint of new molecules (i.e., not used during the model training and validation) and it is well known that the use of a ML model outside its training domain can be risky [2; 3]. In other words, the more distant a point is from the training domain, the more unreliable the prediction. Driven by the motivation to generalize the usage of QSPR/QSAR models for regulatory purposes (e.g., REACH regulation for Registration, Evaluation, Authorization and Restriction of CHemicals), in 2004, the OECD (Organisation for Economic Co-operation and Development) defined a set of five principles for (Q)SAR validation, including the necessity to explicitly define the AD [4]. Nevertheless, this AD definition step is still being overlooked or poorly defined in many studies, as highlighted in [3; 5]. However, knowing if a ML model is extrapolating or not will improve its acceptability and transparency, as is the case when investigating the explainability of a ML model. Indeed, some studies revealed a decrease in extrapolation performance with distance from the training domain, which can be more or less pronounced depending on the ML model [2; 6; 7]. Finally, there is also no clear overview about which method to employ to define the AD in a given problem, especially when dealing with high-dimensional data (e.g., descriptor-based QSPR/QSAR models can contain up to several tens, hundreds or thousands of descriptors). Most classical AD approaches are indeed dedicated to problems with few dimensions (i.e., less than ten), as will be discussed in Section 2. The AD of a model is defined by the structural, physico-chemical and response information contained in the training data used to build the model [4]. Concretely, if a molecule lies outside the AD (i.e., extrapolation case, the molecule has low similarity with the molecules of training data), the prediction is more likely to be unreliable. However, even when properly defined, the AD should be considered cautiously since it does not constitute a strictly delimited space, meaning that the prediction for a molecule inside/outside the AD is not necessarily 100% reliable or false, respectively. Besides, it would be unrealistic to consider the existence of an explicitly defined frontier between reliable and unreliable predictions; one should rather approach this discussion from the viewpoint of a compromise between the size of the AD and the reliability of the predictions. For example, in the leverage method, which is a popular method for defining the AD, as will be described later, the frontier of the AD is generally fixed at a leverage value \(h^{*}\), as defined in Equation (1). However, the strict definition of this unique rule-of-thumb threshold value is not exempt from concerns [8] and, after all, expresses this compromise (i.e., increasing \(h^{*}\) will reduce the reliability of the predictions and vice versa [4]).