## 6 Discussion  
SIMP is considered as one the most widely used approaches for solving TO problems, that, like every structural optimization procedure, is associated with increased demand in computing time and resources. The DLTOP methodology previously developed by the authors of [1], motivated by the insufficiency of SIMP approach, employs deep learning approaches to reduce the number of SIMP iterations, thus achieving a substantial acceleration of the STO problem solution procedure. Specifically, a great amount of SIMP iterations is eliminated by employing a trained DBN, which uses the data generated during the first \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**SIMP**} & \multicolumn{3}{c}{**DLMU/DL-SCALE/DLTOP**} & \multirow{2}{*}{**Acceleration (\%)**} & \multirow{2}{*}{**Reduction (\%)**} \\ \cline{2-3} \cline{5-8}  & **Iterations** & **Objective** & **Time** & & & **Iterations** & **Objective** & **Time** \\ \hline \multicolumn{8}{c}{Example A} \\ \hline DLMU & \multirow{4}{*}{521} & \multirow{4}{*}{242.62} & \multirow{4}{*}{2559.05} & 86 & 244.39 & 495.55 & 80.64 & \(-\)0.73 \\ DL-SCALE & & & & 107 & 246.82 & 670.52 & 73.80 & \(-\)1.73 \\ DLTOP & & & & 141 & 244.96 & 765.96 & 70.07 & \(-\)0.97 \\ \hline \multicolumn{8}{c}{Example B} \\ \hline DLMU & \multirow{4}{*}{367} & \multirow{4}{*}{156.01} & \multirow{4}{*}{1382.55} & 107 & 155.10 & 595.76 & 56.91 & 0.58 \\ DL-SCALE & & & & 90 & 156.08 & 539.94 & 60.95 & \(-\)0.04 \\ DLTOP & & & & 115 & 161.65 & 639.29 & 53.76 & \(-\)3.61 \\ \hline \multicolumn{8}{c}{Example C} \\ \hline DLMU & \multirow{4}{*}{556} & \multirow{4}{*}{112.51} & \multirow{4}{*}{2838.85} & 101 & 112.63 & 604.94 & 78.69 & \(-\)0.11 \\ DL-SCALE & & & & 88 & 112.79 & 561.89 & 80.21 & \(-\)0.25 \\ DLTOP & & & & 121 & 110.56 & 696.58 & 75.46 & 1.73 \\ \hline \multicolumn{8}{c}{Example D} \\ \hline DLMU & \multirow{4}{*}{358} & \multirow{4}{*}{21.79} & \multirow{4}{*}{1306.8} & 99 & 21.79 & 515.14 & 60.58 & \(-\)0.01 \\ DL-SCALE & & & & 86 & 21.76 & 480.23 & 63.25 & 0.12 \\ DLTOP & & & & 165 & 21.82 & 848.38 & 35.08 & \(-\)0.15 \\ \hline \multicolumn{8}{c}{Example E} \\ \hline DLMU & \multirow{4}{*}{573} & \multirow{4}{*}{24.16} & \multirow{4}{*}{2538.61} & 156 & 23.97 & 820.53 & 67.68 & 0.77 \\ DLSCALE & & & & 132 & 24.82 & 737.59 & 70.95 & \(-\)2.73 \\ DLTOP & & & & 220 & 26.35 & 1156.65 & 54.44 & \(-\)9.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the DLMU scheme with the DL-SCALE and DLTOP methodologies for the case of 200,000 number of FE. few iterations to propose a close to final optimized configuration of the design domain, that is then fine-tuned with only a few additional iterations of SIMP. The efficiency of DLTOP stems from the fact that the DBN needs only be trained once and can be subsequently applied to any 2D or 3D STO problem, irrespective of its specifications. Within the scope of further enhancing the computational efficiency of DLTOP, the authors envisioned a novel approach that combines deep learning with reduced-order modeling, which led to the development of the DLMU scheme presented in this paper. Building upon the main principle of DLTOP, the novel DLMU scheme further employs deep learning to extrapolate the results of reduced order models to the full model of the design domain. DLMU thus inherits the benefits of DLTOP, in respect of training and calibrating the DBN only once, while also achieving further acceleration of SIMP via the employment of reduced order models, without compromising the solution quality.