## 5 Conclusions  
The probabilistic design of a retaining wall has been discussed in this paper using different machine learning methods, namely MARS, EmNN, and SOS-LSSVM. The retaining walls are widely used in various infrastructures such as road and bridge construction to stabilize the slopes. A probabilistic analysis against sliding was performed to evaluate the safety of a case study to establish the intelligence prediction model. The input and output datasets were generated based on consideration of uncertainties in soil parameters and fed into the AI models to be trained. Then, the result given by the predictor was assessed based on the performance parameters and graphs such as the Taylor diagram and Regression Error Characteristic curve. For instance, different errors and efficiencies, such as WMAPE, RMSE, MAE, NS, etc., were calculated. Obtained results validate the ability of all three applied advanced methods to evaluate the safety criteria of a cantilever retaining wall with relatively high accuracy. Therefore, the proposed computational intelligence systems can benefit engineers in design and monitoring processes. SOS is an optimization technique for optimizing the parameters of the LSSVM model, and in the current study, it results in a better prediction of the factor of safety. In addition, the reliability index calculated for different optimal models selected gives an overview that SOS-LSSVM is a better model and has outperformed the other two. MARS and EmNN give slightly deviated result, but the POS generated from MARS almost overlaps that of SOS-LSSVM.  
Considering the obtained results, for future works in this field or the design of other geostatructures, SOS-LSSVM can be considered, as its learning rate is optimized using SOS, which gives an upper hand to this algorithm over the other two techniques. In addition, to improve the quality of results, the model can be fed with more training data to ensure better relationships between the input and output dataset. However, future research should study the impact of a higher number of inputs and spatial randomness in the material properties on the performance of suggested AI methods. Finally, it should be stated that this study employed synthetic data to train and validate the machine learning methods. Nevertheless, the proposed methodologies can be applied analogously to realistic problems.  
Conceptualization, P.S. and E.M.; methodology, P.S.; software, P.M. and P.S.; validation, P.M., P.S. and E.M.; formal analysis, P.M.; investigation, P.M.; resources, P.S.; data curation, P.M.; writing--original draft preparation, P.M.; writing--review and editing, E.M.; visualization, P.M.; supervision, P.S.; project administration, E.M. All authors have read and agreed to the published version of the manuscript.  
We acknowledge support by the Open Access Publication Funds of the Ruhr-Universitat Bochum.  
Not applicable.  
Figure 4: Performance curve for models.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.