## 3 Results and Discussions  
As a preliminary step, forward feature selection was performed to optimize the number of predictors. Since the models of our machine learning depend on the number and combination of predictors, estimators such as correlation coefficient (\(\mathbf{R^{2}}\)) and the root mean square error (RMSE) can be the benchmark to evaluate the performance of our  
Figure 1: Graph of nuclear cross-section data of (**a**) \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, (**b**) \({}^{111}\)Cd (p, n) \({}^{111}\)In and (**c**) \({}^{112}\)Cd (p, 2n) \({}^{111}\)In nuclear reactions from various studies used in this work [2; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22] in between 0 and 80 MeV proton incident energy. machine learning. The correlation coefficient (\(\mathbf{R^{2}}\)) measures the closeness of a prediction to the actual value, which is defined as  
\[\mathbf{R^{2}}=1-\frac{\sum_{i=1}^{n}(\mathbf{y}_{i}-\hat{\mathbf{y}_{i}})^{2}}{\sum_{i=1}^{n }(\mathbf{y}_{i}-\langle\mathbf{y}\rangle)^{2}}. \tag{1}\]  
RMSE is defined as  
\[\mathbf{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}(\mathbf{y}_{i}-\hat{\mathbf{y}_{i}})^{2}}{n}}\, \tag{2}\]  
where \(\mathbf{n}\) is the number of observations, \(\mathbf{y}_{i}\) is the actual value, \(\hat{\mathbf{y}_{i}}\) is the predicted value and \(\langle\mathbf{y}\rangle\) is the overall mean. The ideal way to generate nuclear cross-section data is if the models can give an \(\mathbf{R^{2}}\) value close to one and \(\mathbf{RMSE}\) close to zero. Then, we initially removed all of the single point experimental datasets before proceeding with the forward feature selection. When the forward feature selection was applied, more features were added into the feature space sequentially. By manipulating the number of features for the predictors and different combinations of features, the accuracy of the machine can be improved. The number of predictors and combination of predictors along with their respective \(\mathbf{RMSE}\) and correlation coefficients are tabulated in Tables 2-4. Different combinations of predictors are considered for \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, \({}^{111}\)Cd (p, n) \({}^{111}\)In and \({}^{111}\)Cd (p, n) \({}^{111}\)In, respectively, in Tables 2-4. The forward selection step was taken whereby we added features into empty feature space, with the total number of features increasing from 1 to 8, from 1 to 5 and from 1 to 4 for \({}^{109}\)Ag (\(\alpha\), 2n) \({}^{111}\)In, \({}^{111}\)Cd (p, n) \({}^{111}\)In and \({}^{111}\)Cd (p, n) \({}^{111}\)In, respectively. The range of correlation coefficient values, \(\mathbf{R^{2}}\), for all of our predictions is between 0.94 to 0.99, which indicates a good agreement between the prediction and the original data. In Tables 2-4, the optimized number of features (with high \(\mathbf{R^{2}}\) and low \(\mathbf{RMSE}\)) is highlighted. Figure 2 shows the trends of the number of predictors versus the _RMSE_. Intuitively, we may think that the higher the number of features used as predictors is, the higher the correlation coefficient will be and the lower the _RMSE_ of our models will be, since using more datasets to build the models may enhance the prediction. However, these three cases demonstrate that a low _RMSE_ value could be obtained with the use of between one and three features for the machine learning models. This means that only a small number of features are needed to build machine learning models that can generate nuclear cross-section data with good accuracy. Thus, better prediction can be achieved with a small dataset as the input. After the forward selection step, Bayesian optimization was also performed to optimize the hyperparameters of the random forest algorithm of the optimized model. The number of iterations was set to 100 steps. Here, the hyperparameters of the random forest consisted of the number of leaves, number of learners and number of predictors for the random forest, which were set between 1 and 34, between 10 and 500 and between 1 and 4, respectively.