## 3 Proposed Method
### Machine Learning Models  
As mentioned above, the application of deep learning models could produce a good result. However, the generated dataset is relatively small. The authors also do not know of similar sets of initial data of a significant volume or pre-trained models of deep neural networks that solve the problem of calculating the permeability of rocks in uranium deposits, which would allow using the transfer learning technique to tune them. Therefore, the use of deep learning models was considered inappropriate. In the process of the computational experiments, the authors used several types of models: models based on gradient boosting [34] and bagging technique, feed-forward neural networks [16], support vector machines, and, as a reference point (baseline) for comparative analysis, classical regression algorithms (Table 1).  
Figure 3: Data for determining the filtration properties of rocks according to the accepted method.  
The variety of algorithm types provides a broad search for the appropriate type of models. Looking ahead, we note that the ensemble learning methods, and more precisely the gradient boosting models, generally showed the best result.  
To assess the quality of regression models, the following accuracy indicators were used [47]:  
Coefficient of determination (\(R^{2}\));  
Mean square error (mean squared error--\(MSE\));  
Mean absolute error (mean absolute error--\(MAE\));  
Correlation coefficient (\(R\)).  
The quality measures used to evaluate the regression models are listed in Table 2.  
To perform computational experiments, a software system was developed in Python using the numpy, sklearn, matplotlib, cv2, alive_progress, pickle, and tensorflow libraries, which enable the reading and preparing of the initial data, forming a data frame, and applying machine learning models. The computational experiments were performed on a Dell XPS 15 9500 computer equipped with 32 GB of RAM, an Intel(R) Core(TM) i7-10750H processor, and an Nvidia GeForce GTX 1650 Ti discrete graphics card. All equipment is manufactured in China.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Regression Model** & **Abbreviation** & **Method** & **References** \\ \hline XGBoost & XGB & Ensemble learning method based on the gradient boosted trees algorithm. & [35] \\ \hline LightGBM & LGBM & Ensemble learning method based on the gradient boosted trees algorithm. & [36; 37; 38] \\ \hline Random forest & RF & Ensemble learning method based on bagging technique. & [39] \\ \hline Support vector machines & SVM & Method is based on the kernel trick. & [40] \\ \hline Artificial neural network & ANN & Feed forward neural network. & [41; 42] \\ \hline Linear regression & LR & Modeling impact of independent variables to target variable based on linear approach. & [43] \\ \hline Lasso regression & Lasso & Based on the use of such a regularization mechanism that not only helps in reducing over-fitting but can help in feature selection. & [44] \\ \hline Ridge regression & Ridge & A regularization mechanism is used to prevent over-fitting. & [45] \\ \hline Elastic net & elasticnet & Hybrid of ridge regression and lasso regularization. & [46] \\ \hline \end{tabular}
\end{table}
Table 1: Machine learning models.  
\begin{table}
\begin{tabular}{c c c} \hline
**Evaluation Index** & **Equation** & **Explanation** \\ \hline Mean absolute error & \(MAE\ =\frac{\sum_{i=1}^{n}\left(y^{(i)}-h^{(i)}\right)}{n}\) & where n is the sample size; \(y^{(i)}\) is the actual value of the target variable for the i-th sample; \(h^{(i)}\) is the estimated value for the i-th sample. \\ \hline Mean squared error & \(MSE\ =\frac{\sum_{i=1}^{n}\left(y^{(i)}-h^{(i)}\right)}{n}\)\({}^{2}\) & \\ \hline \end{tabular}
\end{table}
Table 2: Evaluation metrics of regression models.