## 2 Materials and Methods
### Development of the Integrated RJD Efficiency Forecasting Method
For the Fm site, the linear discriminant function was as follows (3):  
\[\text{Z}=-0.55\cdot\text{q}_{\text{liq}}-0.102\cdot\text{K}_{\text{comp}}+0.65 \cdot\phi+0.08\cdot\varepsilon_{\text{farfield}}+0.14\cdot\text{P}_{\text{res} }-5.56;\text{R}=0.78 \tag{3}\]  
For the Fm site, 10 of 12 (83%) objects with the relative liquid production increment of less than 6 times were correctly recognized and 11 of 12 (92%) objects with an increment rate more than 6 times were correctly recognized. Based on the revealed parameters, the machine learning models were developed to allow for the forecasting of the liquid production rate after radial jet drilling. Initially, neural networks of different architecture were built, which quite reliably forecasted the liquid production rate after RJD (see Table 3). Figure 4 shows the training results. The second selected forecasting method was the Support Vector Machine method. However, with the modification of the parameters influencing the learning productivity, the best productivity value achieved was 0.79 for the training selection and 0.78 for the test selection with parameters--kernel type = radial basis function, gamma = 0.16, C = 5, epsilon = 0.2. Table 4 shows the models and their corresponding statistical parameters. Where MAPE--mean absolute percentage error; STD--standard deviation; SEM--standard error mean, RMSE--root mean square error. For further forecast, a multi-layer perceptron (MLP) was used, a neural network with a simpler architecture: 17 input layer neurons, 1 hidden layer with 5 neurons, and 1 neuron on the output layer, the neuron activation function is logistic, the error function is the sum of squares. The correlation coefficients achieved for this network were suitable for well stimulation forecasting tasks. Figure 5 shows the difference between the standard statistical method for forecasting well stimulation events efficiency in Perm region and the MLP. A significant improvement in the quality of the forecast can be noted, which makes it possible to determine the potential of wells for RJD. Stage 2. Integrating the machine learning models with the hydrodynamic simulator. The combination of statistical and mathematical forecasting methods significantly increases the reliability of forecasting the effects of well interventions. This approach allows for the taking into account of the geological and technological parameters entered in the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Architecture** & **Training** & **Test** & **Learning** & **Active Hidden** & **Active Output** \\  & **Productivity** & **Productivity** & **Algorithm** & **Error Function** & **Neuron** \\ \hline MLP 17-5-1 & 0.819 & 0.814 & BFGS 27 & Sum of squares & Hyperbolic & Identical \\ MLP 17-5-1 & 0.772 & 0.767 & BFGS 17 & Sum of squares & Exponential & Identical \\ MLP 17-12-1 & 0.798 & 0.807 & BFGS 25 & Sum of squares & Hyperbolic & Identical \\ MLP 17-14-1 & 0.806 & 0.787 & BFGS 20 & Sum of squares & Exponential & Identical \\ MLP 17-5-1 & 0.855 & 0.800 & BFGS 35 & Sum of squares & Exponential & Identical \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Architectures and results of neural networks. machine learning model, as well as the dynamic parameters from the hydrodynamic model at the moment of forecasting. The hydrodynamic simulator selected for the radial jet drilling modeling was Tempest More 8.6. The simulator is a universal hydrodynamic modeling pack used for oil, oil and gas, and gas condensate deposits. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Architecture** & **Training/Test** & **R Square** &
\begin{tabular}{c} **Mean Absolute** \\ **Percentage Error (MAPE)** \\ \end{tabular} & **STD** & **SEM** & **RMSE** \\ \hline MLP 17-5-1 & training & 0.74 & 13\% & 4.36 & 0.64 & 3.8 \\ MLP 17-5-1 & test & 0.65 & 16.2\% & 4.16 & 0.66 & 5.8 \\ SVM & training & 0.62 & 17.02\% & 3.5 & 0.26 & 5.01 \\ SVM & test & 0.61 & 17.07\% & 3.7 & 0.48 & 5.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical measures of the proposed models.