**4. Conclusions**

The self-adaptive differential evolution (*SADE*) algorithm was implemented to determine the best combination of ANN parameters to predict the static Poisson's ratio with a high accuracy. Comparing the results obtained from the developed ANN model with the *PRstatic* values measured in the laboratory demonstrates the following:


**Author Contributions:** Conceptualization, S.E., A.A. and T.M.; methodology, T.M., A.G.; software, T.M.; validation, S.E., A.G. and A.A.; formal analysis, S.E. A.G.; investigation, A.A.; resources, S.E.; data curation, S.E., A.A.; writing—original draft preparation, A.G.; writing—review and editing, A.A., S.E.; visualization, T.M., A.A.; supervision, S.E.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors wish to acknowledge King Fahd University of Petroleum and Minerals (KFUPM) for use of various facilities in carrying out this research. Many thanks are due to the anonymous referees for their detailed and helpful comments.

**Conflicts of Interest:** The author declares no conflict of interest.

### **Nomenclature**


#### **Appendix A**

The formula of correlation coefficient (*R*) between any two variables (*x*, *y*) used in this study is expressed as:

$$R = \frac{k\sum\_{i=1}^{k} xy - \left(\sum\_{i=1}^{k} \chi\right)\left(\sum\_{i=1}^{k} y\right)}{\sqrt{k\left(\sum\_{i=1}^{k} \chi^2\right) - \left(\sum\_{i=1}^{k} y\right)^2} \sqrt{k\left(\sum\_{i=1}^{k} y^2\right) - \left(\sum\_{i=1}^{k} y\right)^2}}$$

where *K* is the number of dataset points.

Mean absolute percentage error (MAPE) is expressed as:

$$MAPE = \frac{\sum \left| \frac{PR\_{static,measured} - PR\_{static,predicted}}{PR\_{static,measured}} \right| \times 100\% \times 100\%}{m}$$

where *m* is the number of dataset points.

Coefficient of determination (*R*2)

$$R^2 = \left(\frac{k\sum\_{i=1}^k xy - \left(\sum\_{i=1}^k x\right)\left(\sum\_{i=1}^k y\right)}{\sqrt{k\left(\sum\_{i=1}^k x^2\right) - \left(\sum\_{i=1}^k y\right)^2}\sqrt{k\left(\sum\_{i=1}^k y^2\right) - \left(\sum\_{i=1}^k y\right)^2}}\right)^2$$

#### **References**


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