## 5 Conclusions  
The article presents the procedure for developing an artificial neural network (ANN) model. The potential of using an ANN to increase the confidence level of the prediction of the damping ratio (D) of normally and lightly overconsolidated Quaternary cohesive soil was described. Careful selection of the input variables describing the problem at hand is necessary in order to balance the complexity of the issue at hand with the amount of information available. Minor variables were omitted. The mean absolute error (MAE) for the performed tests was 0.1854, while the mean square error (MSE) was 0.1704. The predicted values of the damping ratio of clay soils are characterized by high convergence (coefficient of determination, R\({}^{2}\) = 0.976).  
Comparing the ANN model with other published empirical formulas shows an improvement in the prediction accuracy. It is not possible to reliably evaluate the damping ratio for the tested cohesive soil with the use of commonly known empirical equations. A comparison of the measured and calculated value with equations from the literature gave a very large spread of the damping ratio and large error values. The conducted analysis shows that it can be concluded that an empirical model should be applied to the soil, with a similar genesis and mineral composition as the soil for which they were created. Considering the problem, it was shown that artificial neural networks are more flexible compared to formulas and relationships with a predetermined structure. Additionally, another advantage of artificial neural networks is the possibility to further model generalization by inserting newer records and the automatic adaptation of the architecture.  
Artificial neural networks are well suited to modeling the complex behavior of most geotechnical engineering materials, which, by their very nature, exhibit extreme variability. The use of artificial neural networks to predict the damping ratio of clay soils is an effective, highly efficient, and easy-to-use method.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **[PERSON] and** & **[PERSON] and** & **[PERSON]** & **[PERSON] et al. [39],** & **[PERSON] et al. [29]** & **Authors ANN** \\  & **[PERSON] [36],** & **[PERSON] [37],** & **Equation (3)** & **Equation (4)** & **Equation (5)** & **Equation (6)** & **Model** \\ \hline MAE & 3.63 & 1.02 & 1.06 & 1.77 & 0.45 & 0.19 \\ R\({}^{2}\) & 0.21 & 0.79 & 0.78 & 0.77 & 0.96 & 0.98 \\ \hline \end{tabular}
\end{table}
Table 8: The comparison of mean absolute error (MAE) and determination coefficient (R\({}^{2}\)) for analyzed models.  
**Author Contributions:** Conceptualization, M.L.-S. and K.Z.; methodology, K.Z. and E.S.; laboratory tests, K.Z.; data analysis, K.Z. and E.S.; writing--original draft preparation, K.Z., A.M. and G.W.; supervision, A.M. and G.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that were used to support the findings of this study are included within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.