# Prediction of Swelling Index Using Advanced Machine Learning Techniques for Cohesive Soils
## 5 Conclusions  
This study set out to optimize the swelling index parameter conducted by the expensive and time-consuming Oedometer test, contributing to elaborating on a new accurate model for predicting the swelling index (\(C_{s}\)) from easily obtained geotechnical physical parameters. To achieve our aim, several advanced machine learning methods were used for a practical analysis aimed at modeling the physical parameters including the wet density (\(Y_{h}\)), the dry density (\(Y_{d}\)), the degree of saturation (\(Sr\)), the plasticity index (\(PI\)), the water content (\(w\)), the void ratio (\(e\)), the liquid limit (\(WL\)), sample depth (\(Z\)), and the fine contents (\(FC\)). Firstly, principal component analysis (\(PCA\)), Gamma test (\(GT\)), and the forward selection (\(FS\)) approach are utilized to reduce the input variable numbers and choose the optimal ones. The results indicate the reduction of nine input variables to four (using \(FS\) and \(GT\)) and three (using \(PCA\) techniques). Afterward, the advanced machine learning techniques have applied for modeling the proposed optimal inputs and their accuracy models were evaluated through six statistical indicators (MAE, RMSE, IOS, NSE, R, and IOA). The comparison of results assessment between different proposed models revealed the superiority of the \(FS\)-\(RF\) model, which gives the highest accuracy in terms of \(MAE\) (\(5.6\times 10^{-3}/10.6\times 10^{-3}\)), \(RMSE\) (\(0.007\) / \(0.013\)), \(IOS\) (\(0.165\) / \(0.298\)), \(NSE\) (\(0.75\) / \(0.13\)), \(R\) (\(0.94\) / \(0.71\)), and \(IOA\) (\(0.95\) / \(0.82\)) during the training/validation phase. For assessing the predictive capacity of the proposed \(FS\)-\(RF\) model, the K-fold cross validation approach with \(K\) = 10 has been carried out. The results show that this model has a high correlation coefficient, ranging between 0.92 and 0.94 for training data, and 0.62 to 0.75 for validation data in the 10 splits, meaning that any over-fitting or under-fitting have been found. Three criteria were used to compare the performances of the most appropriate \(FS\)-\(RF\) model with the proposed formulas in the literature: the mean, the standard deviation, and the Box plot of the ratio \(C_{s,estimated}/C_{s,measured}\). The findings indicate that the aforementioned \(FS\)-\(RF\) model is more effective than the empirical formulae. Finally, a sensitivity analysis was carried out in order to assess the impacts of the soil parameter inputs on the model performance. The results proved that \(WL\) has the most important effect on the prediction of \(C_{s}\). \(PI\) has a moderate influence and ranked second. In addition, \(W\) and \(Y_{d}\) have little effect on \(C_{s}\). In the future studies, it is recommended that meta-heuristic algorithms be undertaken, like Particle Swarm Optimization (_PSO_) and Gravitational Search Algorithm (_GSA_), Biogeography-Based Optimization (_BBO_), Whale Optimization Algorithm (_WOA_), AntColony Optimization (_ACO_), and Grey Wolf Optimizer (_GWO_). These algorithms have proved high performance results combined with the machine learning techniques leading to improving their learning and rapidly converging to the best solution. Conceptualization, M.A.B. ; methodology, M.A.B. ; software, M.A.B. ; validation, M.A.B. and A.-I.P. ; formal analysis, M.A.B. ; investigation, M.A.B. ; resources, M.A.B. ; data curation, M.A.B. ; writing--original draft preparation, M.A.B. and A.-I.P. ; writing--review and editing, M.A.B. and A.-I.P. ; visualization, M.A.B. and A.-I.P. ; supervision, M.A.B. and A.-I.P. ; project administration, M.A.B. ; funding acquisition, M.A.B. and A.-I.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Restrictions apply to the availability of these data.