## 3 Simulation Results
### Prediction Based on Static Data
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Method**} & \multicolumn{6}{c}{**Endpoint Relative Error in Testing (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{  }}}}}}}}}}}}}}\))} & \multicolumn{10}{c}{**Analepoint Absolute Error in Testing (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}}\))**} \\ \multicolumn{1}{c}{**Modeling \#**} & \multicolumn{1}{c}{**Average**} & \multicolumn{10}{c}{**Modeling \#**} \\ \hline  & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 5 & 9 & 10 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 0 \\ \hline SVR (polynomial kernel) & 15.12 & 22.84 & 11.25 & 33.32 & 17.05 & 44.21 & 17.23 & 4.83 & 11.91 & 8.88 & 15.13 & 0.087 & 0.010 & 0.006 & 0.004 & 0.008 & 0.001 & 0.002 & 0.005 & 0.001 & 0.014 & 0.027 & 0.005 & 0.005 \\ SVR (Gaussian kernel) & 14.39 & 18.14 & 17.25 & 9.81 & 6.27 & 1.30 & 16.21 & 12.33 & 1.70 & 10.92 & 0.003 & 0.000 & 0.0054 & 0.002 & 0.004 & 0.002 & 0.005 & 0.004 & 0.003 & 0.003 & 0.000 & 0.004 \\ SVR (Gaussian kernel) & 20.52 & 15.39 & 13.00 & 13.00 & 33.92 & 14.88 & 2.07 & 14.63 & 20.93 & 20.58 & 19.87 & 0.089 & 0.009 & 0.001 & 0.001 & 0.012 & 0.004 & 0.005 & 0.005 & 0.009 & 0.005 & 0.0073 \\ MARS ( piecewise-linear) & 0.67 & 15.79 & 13.80 & 15.32 & 14.88 & 2.07 & 17.32 & 12.85 & 5.56 & 11.99 & 0.000 & 0.009 & 0.004 & 0.004 & 0.005 & 0.001 & 0.001 & 0.001 & 0.000 & 0.002 & 0.001 & 0.001 \\ MARS ( piecewise-cubic) & 2.66 & 15.99 & 13.70 & 15.38 & 3.64 & 15.84 & 15.87 & 15.23 & 15.49 & 15.76 & 15.28 & 0.000 & 0.003 & 0.005 & 0.001 & 0.001 & 0.005 & 0.007 & 0.002 & 0.007 & 0.003 & 0.004 \\ KANN ( piecewise-cubic) & 5.46 & 15.79 & 18.58 & 16.57 & 7.45 & 15.82 & 15.00 & 15.62 & 16.27 & 17.28 & 0.003 & 0.002 & 0.004 & 0.004 & 0.005 & 0.005 & 0.005 & 0.009 & 0.002 & 0.007 & 0.003 & 0.001 & 0.004 \\ RF & 5.42 & 18.74 & 15.80 & 18.84 & 8.39 & 10.25 & 3.01 & 19.77 & 7.82 & 12.00 & 11.89 & 0.002 & 0.008 & 0.009 & 0.004 & 0.005 & 0.005 & 0.003 & 0.001 & 0.005 & 0.0034 & 0.0042 & 0.0041 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Absolute and relative errors on selected meltings in carbon prediction based on static data. \begin{table}
\begin{tabular}{l l l} \hline
**BF** & **Equation** & **BF** & **Equation** \\ \hline BF1 & C(\(x_{15}\)\(|\)\(-\)\(1\), \(367.76\), \(735.52\), \(984.31\)) & BF12 & BF5 \(\times\) C(\(x_{15}\)\(|\)\(+\)\(1\), \(83650\), \(147100\), \(157750\)) \\ BF2 & C(\(x_{10}\)\(|\)\(-\)\(1\), \(0.003\), \(0.006\), \(0.052\)) & BF13 & BF5 \(\times\) C(\(x_{15}\)\(|\)\(-\)\(1\), \(83650\), \(147100\), \(157750\)) \\ BF3 & C(\(x_{2}\)\(|\)\(+\)\(1\), \(5294.8\), \(7856.6\), \(8392.6\)) & BF14 & BF11 \(\times\) C(\(x_{13}\)\(|\)\(-\)\(1\), \(597,\) \(1194\), \(2171.5\)) \\ BF4 & C(\(x_{2}\)\(|\)\(-\)\(1\), \(52948\), \(7856.6\), \(8392.6\)) & BF15 & BF3 \(\times\) C(\(x_{1}\)\(|\)\(+\)\(2\), \(0.2045\), \(0.306\), \(31858\)) \\ BF5 & C(\(x_{2}\)\(|\)\(+\)\(1\), \(18900\), \(37800\), \(46 Similarly, the piecewise-cubic MARS model was the most effective in predicting carbon content on unknown data, and its equation is as follows:  
\[