# Application of Soft Computing Techniques for Predicting Thermal Conductivity of Rocks
## 5 Conclusions  
In our study, a literature survey was performed to the establishment of the dataset for estimating the thermal conductivity of rock via several rock properties, including the UCS, density, porosity, and P-wave velocity of rocks. Several simple variable regressions were conducted among the rocks' properties and TC. As a result of simple regressions, we found that the P-wave velocity and density had the highest and the lowest effect on the TC, respectively. Further, the relationships between porosity and density and between UCS and P-wave velocity were then considered significant and meaningful. To estimate TC via rock properties, two empirical equations were developed. First, a model was developed using NLMR, and then a second model was developed by GEP. The two statistical indices R\({}^{2}\) and RMSE were utilized to evaluate the robustness of the developed models in order to predict TC. While the GEP model had a higher value of the R\({}^{2}\) (0.95) and a lower value of RMSE (0.17), a low R\({}^{2}\) (0.82) and RMSE (0.32) were obtained for NLMR. A comparison of the performance indices of the proposed models and of the previously published models revealed that the GEP and NLMR models were able to produce more accurate predictions. As a result, the developed model can be used for estimating the TC of rocks, since performing TC-related tests might be time-consuming and cost-restrictive. Additionally, despite the fact that our study proposed methods and mathematical models that significantly increased prediction accuracy, there are some associated limitations. As mentioned in previous sections, a limited number of datasets were used in our study because data collection in geosciences is challenging. As a result, we recommend that future studies focus on rocks and parameter ranges that overlap only slightly with those  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **RMSE** & **Rank** \\ \hline New GEP model (Equation (9)) & 0.92 & 0.21 & 1 \\ New NLMR model (Equation (4)) & 0.82 & 0.32 & 2 \\ MVRA [47] (Equation (10)) & 0.74 & 0.39 & 3 \\ MVRA [24; 71] (Equation (11)) & 0.35 & 0.62 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performance indices and ranking of the new and the previous TC predictor models calculated for all 50 datasets.  
of this study. Our study and similar studies have not quantified the texture of the rocks, which is one of the most important parameters. The data collection and analysis stages of future studies should incorporate this parameter.  
Conceptualization, M.S. and S.Y.; methodology, M.S. and S.Y.; software, M.S.; formal analysis, M.S., A.A. and S.Y.; resources, M.S., A.A. and S.Y.; data curation, M.S. and S.Y.; writing--original draft, M.S., T.M., A.A., S.Y. and M.M.S.S.; writing--review and editing, M.S., T.M., A.A., S.Y. and M.M.S.S.; supervision, S.Y.; funding acquisition, M.M.S.S. All authors have read and agreed to the published version of the manuscript.  
The research was partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program 'Priority 2030' (Agreement 075-15-2021-1333, dated 30 September 2021).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.