## 5 Deep Neural Network Framework
### Evaluation of Proposed DNN Models
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Hidden Layers**} & \multirow{2}{*}{**Neurons**} & \multirow{2}{*}{**Epochs**} & \multicolumn{6}{c}{\(M_{br,max}\)} & \multicolumn{6}{c}{\(M_{br,min}\)} \\ \cline{5-10}  & & & & \(R^{2}\) & **RMSE** & **MSE** & **MAE** & \(R^{2}\) & **RMSE** & **MSE** & **MAE** \\ \hline H3N50E100 & 3 & 50 & 100 & 0.723 & 501,974 & \(2.52\times 10^{11}\) & 305,974 & 0.474 & 208,982 & \(4.37\times 10^{10}\) & 147,171 \\ H3N50E200 & 3 & 50 & 200 & 0.747 & 480,275 & \(2.31\times 10^{11}\) & 296,841 & 0.543 & 195,618 & \(3.83\times 10^{10}\) & 138,242 \\ H3N100E100 & 3 & 100 & 100 & 0.749 & 477,061 & \(2.28\times 10^{11}\) & 293,478 & 0.583 & 185,885 & \(3.46\times 10^{10}\) & 127,637 \\ H3N100E200 & 3 & 100 & 200 & 0.807 & 418,479 & \(1.75\times 10^{11}\) & 256,186 & 0.639 & 172,947 & \(2.99\times 10^{10}\) & 117,676 \\ H3N200E100 & 3 & 200 & 100 & 0.802 & 425,512 & \(1.81\times 10^{11}\) & 159,758 & 0.659 & 169,799 & \(2.88\times 10^{10}\) & 115,709 \\ H3N200E200 & 3 & 200 & 200 & 0.908 & 295,307 & \(8.72\times 10^{10}\) & 163,460 & 0.747 & 147,600 & \(2.18\times 10^{10}\) & 958,91 \\ H4N50E100 & 4 & 50 & 100 & 0.859 & 364,493 & \(1.33\times 10^{11}\) & 220,826 & 0.659 & 168,732 & \(2.85\times 10^{10}\) & 112,310 \\ H4N50E200 & 4 & 50 & 200 & 0.913 & 281,904 & \(7.95\times 10^{10}\) & 175,535 & 0.697 & 158,435 & \(2.51\times 10^{10}\) & 105,033 \\ H4N100E100 & 4 & 100 & 100 & 0.932 & 250,220 & \(6.26\times 10^{10}\) & 150,478 & 0.748 & 144,280 & \(2.08\times 10^{10}\) & 960,34 \\ H4N100E200 & 4 & 100 & 200 & 0.981 & 135,862 & \(1.85\times 10^{10}\) & 908,07 & 0.863 & 109,627 & \(1.2\times 10^{10}\) & 707,01 \\ H4N200E100 & 4 & 200 & 100 & 0.982 & 137,643 & \(1.89\times 10^{10}\) & 873,24 & 0.859 & 108,873 & \(1.19\times 10^{10}\) & 687,04 \\ H4N200E200 & 4 & 200 & 200 & 0.992 & 855,97 & \(7.33\times 10^{9}\) & 530,85 & 0.973 & 486,15 & \(2.36\times 10^{9}\) & 299,56 \\ H5N50E100 & 5 & 50 & 100 & 0.951 & 223,183 & \(4.98\times 10^{10}\) & 143,079 & 0.779 & 136,631 & \(1.87\times 10^{10}\) & 913,89 \\ H5N50E200 & 5 & 50 & 200 & 0.978 & 144,863 & \(2.1\times 10^{10}\) & 977,20 & 0.837 & 116,433 & \(1.36\times 10^{10}\) & 788,44 \\ H5N100E100 & 5 & 100 & 100 & 0.982 & 137,411 & \(1.89\times 10^{10}\) & 876,67 & 0.913 & 857,49 & \(7.35\times 10^{9}\) & 548,41 \\ H5N100E200 & 5 & 100 & 200 & 0.991 & 989,19 & \(9.79\times 10^{9}\) & 660,66 & 0.972 & 494,90 & \(2.45\times 10^{9}\) & 336,42 \\ H5N200E100 & 5 & 200 & 100 & 0.989 & 109,128 & \(1.19\times 10^{10}\) & 704,50 & 0.977 & 502,29 & \(2.52\times 10^{9}\) & 332,95 \\
**H5N200E200** & **5** & **200** & **200** & **0.993** & **791,70** & **6.27\(\times\)\(10^{9}\)** & **496,36** & **0.990** & **304,57** & **9.28\(\times\)\(10^{8}\)** & **200,61** \\ \hline \hline \end{tabular} Note that the best prediction model for \(M_{br}\) is H5N200E200.  
\end{table} 
Table 9: Accuracy of DNN models for \(M_{br}\) using various performance criteria. Figure 9: Comparisons of training and validation loss of bracing moments (\(M_{br,max}\), \(M_{br,min}\)): (**a**) 3-50-200; (**b**) 3-100-200; (**c**) 3-200-200; (**d**) 4-50-200; (**e**) 4-100-200; (**f**) 4-200-200; (**g**) 5-50-200; (**h**) 5-100-200; and (**i**) 5-200-200 (in which 3-50-200 means a DNN model with three hidden layers, 50 neurons for each hidden layer, and 200 epochs).