## 5 Conclusions and Further Studies
and S.S.; Writing--Review and Editing, L.D., H.J. and S.S.; Funding Acquisition, H.J. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Research Foundation of Korea (NRF) (No. NRF-2019R1G1A1010335). The authors declare no conflict of interest. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Weights**} & \multicolumn{2}{c}{**Biases**} \\ \hline \(\mathbf{R}_{\text{CFNN}}^{\text{\emph{mean}}}\) & \(\left(\mathbf{z}_{\text{CFNN}}^{\text{\emph{mean}}}\right)^{T}\) & \(\left(\mathbf{q}_{\text{CFNN}}^{\text{\emph{mean}}}\right)^{T}\) & \(\mathbf{c}_{\text{CFNN}}^{\text{\emph{mean}}}\) & \(\mathbf{q}_{\text{CFNN}}^{\text{\emph{mean}}}\) \\ \hline
3.4680 & 4.5940 & & 0.5890 & \(-\)5.7880 & \\
4.7000 & 3.4200 & & \(-\)0.1830 & \(-\)5.0120 & \\ \(-\)3.5790 & 4.9050 & & 0.5820 & 3.9430 & \\
5.2270 & 2.2140 & & \(-\)0.1130 & \(-\)3.7440 & \\
1.5730 & \(-\)5.5360 & & 0.2110 & \(-\)2.9200 & \\ \(-\)4.3610 & 3.8520 & & \(-\)0.5380 & 2.0050 & \\ \(-\)2.6110 & 5.1060 & & \(-\)0.2640 & 1.4290 & \\
1.3240 & 5.6320 & \(-\)0.2540 & \(-\)0.3850 & \(-\)0.8230 & \\
5.0350 & 2.7780 & 0.3700 & \(-\)0.2030 & 0.3890 & \(-\)0.3310 \\
5.1120 & 2.6770 & & 0.03700 & 0.7280 & \\ \(-\)5.4880 & \(-\)1.8040 & & \(-\)0.0510 & \(-\)1.4370 & \\
5.4600 & 1.8770 & & 0.1170 & 2.1230 & \\
4.5330 & \(-\)3.4080 & & 0.3510 & 3.1740 & \\ \(-\)0.6110 & 5.8300 & & 0.0350 & \(-\)3.4760 & \\
3.1690 & \(-\)4.8040 & & \(-\)0.3720 & 4.4170 & \\ \(-\)4.9220 & \(-\)3.0140 & & \(-\)0.0030 & \(-\)5.0410 & \\ \(-\)0.9670 & \(-\)5.6650 & & \(-\)0.5560 & \(-\)5.7940 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated parameter values (Weight and bias) of the proposed CFNN for mean function in simulation study 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{3}{c}{**a. Mean Function**} & \multicolumn{3}{c}{**b. Standard Deviation Function**} \\ \hline \multicolumn{3}{c}{**Weights**} & \multicolumn{3}{c}{**Biases**} & \multicolumn{3}{c}{**Weights**} & \multicolumn{3}{c}{**Biases**} \\ \hline \multicolumn{3}{c}{\(\mathbf{V}_{RBFN}^{mean}\)} & \multicolumn{1}{c}{\(\mathbf{(u_{RBFN}^{mean})}^{T}\)} & \multicolumn{1}{c}{\(\mathbf{e_{RBFN}^{mean}}\)} & \multicolumn{1}{c}{\(\mathbf{f_ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Weights**} & \multicolumn{3}{c}{**Biases**} \\ \hline  & \(\mathbf{R_{CFNN}^{std}}\) & & \(\left(\mathbf{z_{CFNN}^{std}}\right)^{T}\) & \(\left(\mathbf{q_{CFNN}^{std}}\right)^{T}\) & \(\mathbf{c_{CFNN}^{std}}\) & \(\mathbf{d_{CFNN}^{std}}\) \\ \hline
2.0800 & 2.0450 & 1.7150 & & 0.8060 & \(-2.7520\) & \\
1.3360 & 2.1850 & 1.1350 & & 0.0190 & \(-3.1570\) & \\ \(-2.1980\) & \(-0.2670\) & 1.5240 & & 0.0550 & 2.4750 & \\
1.6410 & 1.7640 & 2.2460 & & \(-0.5140\) & \(-1.7790\) & \\
0.9380 & \(-2.5720\) & 1.7050 & \(-0.4480\) & 0.1360 & \(-0.7120\) & \\ \(-3.1130\) & \(-0.7290\) & 0.9550 & \(-0.6100\) & \(-0.4490\) & 0.6660 & \(-0.0920\) \\
0.8410 & 2.7640 & 1.8200 & 0.7170 & 0.4000 & \(-1.2890\) & \\
0.9370 & 2.2670 & \(-1.8640\) & & 0.8030 & 0.9310 & \\
1.7920 & 2.1840 & 1.0390 & & \(-0.0180\) & 1.7790 & \\
2.2030 & 0.7220 & \(-2.3830\) & & 0.0520 & 2.2580 & \\ \(-1.8960\) & \(-2.6360\) & \(-0.6560\) & & 0.0710 & \(-2.9400\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Estimated parameter values (Weight and bias) of the FFNN for standard deviation function in the case study.