## 2 Materials and Methods
### Building the Dataset and Evaluation of the Models  
In this study, the previously mentioned algorithms outlined in Section 2.2 are utilized to construct developed models to predict the applied stress and dry unit required to achieve the lowest swell amplitude in expansive soil. To formulate these models, various geotechnical identification parameters of expansive soil will be introduced as inputs to the machine learning models. These parameters include the liquid limit (_LL_), initial degree of saturation (SR), maximum dry unit weight (\(\gamma_{dmax}\)) as determined by the standard Proctor test, and the dry unit weight (\(\gamma_{d}\)) to predict the optimal applied stress (\(\sigma_{min}\)), while the parameters including liquid limit (_LL_), initial degree of saturation (SR), maximum dry unit weight (\(\gamma_{dmax}\)), and the applied stress (\(\sigma\)) will be used to predict the optimal dry unit weight (\(\gamma_{max}\)) as shown in Table 3. The output parameter will be the applied stress and dry unit weight required to achieve the lowest level of swell amplitude (almost zero) in expansive soil. In evaluating the effectiveness of the developed models, the initial step involves subjecting them to scrutiny using the training data. Subsequently, to assess the models' generalization capabilities, the method of 'Cross-Validation' is employed. This involves testing the models with datasets distinct from those used during the training phase. In this research, a total of 657 datasets were used in developing each predictive model, specifically designed to estimate the applied stress needed to achieve minimal volumetric changes. Among these datasets, 70% were allocated for the training phase, while the remaining 30% were carefully reserved for the crucial purposes of validation and testing, employing the Cross-Validation methodology. The dataset used in this study comprises 657 systematically curated entries, enhancing the precision of our machine learning models. Specifically, 648 entries were generated  
Figure 11: An example of a visualized neural network plot with two hidden layers of five neurons each and four features. from experimental findings, systematically covering various parameters such as sand percentages, initial degrees of saturation, and dry unit weights. For each sand percentage, 16 samples, corresponding to unique liquid limits, were generated. Within each degree of saturation, four initial dry unit weights were considered, resulting in 16 samples for each percentage. Each sample underwent replication four times and testing with applied stress values (25-300 kPa) to identify dry unit weight and stress levels nullifying swell amplitude. To address the significant impact of applied stress on predictive accuracy, we employed a condensed approach for each sand percentage. This involved deriving trendline equations capturing the relationship between applied stress and the corresponding dry unit weight, with the goal of nullifying swell amplitude for each saturation degree. These equations enabled the projection of dry unit weights across a range of stress values (25-300 kPa) in systematic 10 kPa intervals. The dataset was thus expanded to encompass 27 consolidated stress levels, each multiplied by four initial saturation degrees and further multiplied by six distinct sand percentages, resulting in the generation of 648 datasets. Additionally, nine data points from previous research by [PERSON] [82] and [PERSON] [83] were included, contributing to the compilation of 657 systematically curated datasets. During the training, validation, and testing process of the models, the performance was evaluated by calculating the root mean square error (RMSE) (Equation (1)), mean absolute error (MAE) (Equation (2)), and the coefficient of determination (R\({}^{2}\)) (Equation (3)). The RMSE is the root of average squared difference between the predicted outputs and the actual targets, where a lower RMSE value indicates better performance.