## 3 Results and Discussion
### Comparative Model Performance  
The performance of different machine learning or deep learning algorithms may vary depending on the datasets. Generally, deep learning algorithms outperform shallow machine learning techniques. To validate this statement, four machine learning models, which are gradient boosting (GB), K-nearest neighbor (KNN), random forest (RF), and support vector machine (SVM), were developed for the SRT problem using the same dataset as in Table 2.  
All those four machine learning models are supervised learning which commonly used to solve a classification problem but still can be used for regression. The details of four comparative models are shown in Table 11. The model validation results for the slurry test can be seen in Tables 12-16, while Table 14 is the result of the sand pack test.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Description** & **Hyperparameter (value)** & **Formula** \\ \hline \multirow{5}{*}{GB} & \multirow{5}{*}{GB’s prediction used ensemble method with gradient descent to minimize the loss function [55].} & Loss function [classification: binary\_crossentropy, regression: (east\_squares) & \(\hat{F}=\operatorname*{argmin}_{F}\mathbb{E}_{x_{g}}[L(y,F(x))]\) \\ \cline{3-4}  & & Learning rate (0.1) & \(L(y,F(x))\) is the loss function; margin is \\ \cline{3-4}  & & Maximum number of trees (100) & the argument of function \(F\) that minimizes the expected value of loss function. \\ \cline{3-4}  & & Maximum number of samples per leaf (20) & \\ \hline \multirow{5}{*}{KNN} & \multirow{5}{*}{KNN cast the prediction by the weighted average of the targets according to its neighbor’s closest distance [56].} & Number of neighbors (3) & \(y(d_{i})=\operatorname*{argmax}_{k}\sum_{j\in\NN}y(x_{j},c_{k})\) \\ \cline{3-4}  & & Weight function used for prediction (uniform) & \(d_{i}\) is a test example; \(x_{j}\) is one of the KNN in training set; \(y(x_{j},c_{k})\) is an indicator that the training set; \(x_{j}\) belongs to class \(c_{k}\) \\ \cline{3-4}  & & Leaf size (30) & training set, \(x_{j}\) belongs to class \(c_{k}\) \\ \cline{3-4}  & & Power parameter (2) & \(x_{k}\) is the argument of function \(k\) that gives the maximum predicted probability. \\ \cline{3-4}  & & Distance metric used for the tree (minkowski) & \\ \hline \multirow{5}{*}{RF} & \multirow{5}{*}{RF represents a boosting method consisting of a collection of decision trees where a majority vote acquires the prediction over each tree’s predictions [57].} & Number of features to consider when looking for the best split (auto) & Random state (42) \\ \cline{3-4}  & & Regularization parameter (1) & \\ \cline{3-4}  & & Kernel (classification: linear, regression: RBF) & \(R(y,b)=C\times\frac{\kappa}{\mu-1}\ell(y_{i},f(x_{i}))+\frac{1}{||w||^{2}}\) \\ \cline{3-4}  & & Stopping criteria tolerance (\(1\times 10^{-3}\)) & C is the regularization parameter; \\ \cline{3-4}  & & Hard limit on iterations within solver (\(-1\)) & \(\ell(y_{i},f(x_{i}))\) is the loss function; \(||w||\) is the hyperplane with a maximum margin. \\ \cline{3-4}  & & Kernel coefficient for RBF [regression only: scale] & \\ \cline{3-4}  & & Epsilon (regression only: 0.1) & \\ \hline \hline \end{tabular}
\end{table}
Table 11: The details of four comparative models.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **TN** & **FP** & **FN** & **TP** & **Accuracy** \\ \hline
1D-CNN & 41 & 1 & 1 & 6 & 0.959 \\ \hline GB & 35 & 1 & 2 & 3 & 0.927 \\ \hline KNN & 34 & 1 & 2 & 4 & 0.927 \\ \hline RF & 33 & 2 & 3 & 3 & 0.878 \\ \hline SVM & 31 & 2 & 4 & 4 & 0.854 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Comparative model validation result of the slurry test with PLUG_SIGN as the output.  
The results showed that the 1D-CNN model outperformed all four machine learning models for both the slurry and sand pack tests. It justifies that deep learning algorithms perform better than shallow machine learning methods.