## 4 Conclusions  
In this work, a method was presented to train an ANN using online deep learning and use it to solve optimization problems. In the context of the paper, TO was chosen as the problem to be solved. The ANN in charge of generating topology-optimized geometries does not need any pre-optimized data for the training. The generated geometries are, in most cases, very similar to the results of conventional topology optimization, according to [PERSON] or [PERSON] et al. This topology optimizer is much faster, due to the fact that the computing-intensive part is shifted into the training. After the training, the artificial neural network based topology optimizer is able to deliver geometries that are nearly identical to the ones generated by conventional topology optimizers. This is achieved by using a new approach: the predictor-evaluator network (PEN) approach. PEN consists of a trainable predictor that is in charge of generating geometries, and evaluators that have the purpose of evaluating the output of the predictor during the training. The method was tested for the 2D case up to an output resolution of \(64\times 64\). This choice is not a limitation of the method and can be improved by using better hardware for training or by high-performance computing. The use of the method for the 3D case and higher resolutions is conceivable. The optimization of the computational efficiency of the training phase was not the first priority of this project since the training is performed just once and, therefore, affects the performance of the method only in a limited fashion. A critical step is the calculation of the displacements in the compliance evaluator. The use of faster algorithms (e.g., sparse solvers) could remove the mentioned limitations. One approach to improve the learning process would be to train only in areas where there is a high potential for improvement, through appropriate selection of training data points. The results of the PEN method are comparable to the ones of the conventional method. However, the PEN method could prove superior in handling applications and optimization \begin{table}
\begin{tabular}{l l} \hline \hline \(t_{\text{P}}\) & 7.3 ms \\ \(t_{\text{TO}}\) & 1.9 s \\ \(e_{\text{BEP}}\) & 6226 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Time comparison of conventional and predictor-evaluator network (PEN) based methods at a resolution of \(64\times 64\). problems of higher complexity, such as stress limitations, compliant mechanisms and many more. This expectation is related to the fact that no optimized data are needed. All methods that process pre-optimized data suffer from the difficulties encountered by conventional optimization, while managing the above-mentioned problems. Because the PEN method works without optimized data, it could also be applied to problems that have no optimal solutions or solutions that are hard to calculate, such as the fully stressed truss optimization. To date, variable kinematic boundary conditions have not been tested. This will be done in future research, together with resolution improvement and application to three-dimensional design domains and different optimization problems. Conceptualization, A.H. ([PERSON]); data curation, A.H. ([PERSON]); formal analysis, A.H. ([PERSON]) and L.F.C. ; investigation, A.H. ([PERSON]); methodology, A.H. ([PERSON]); project administration, A.H. ([PERSON]) and A.H. ([PERSON]); resources, A.H. ([PERSON]) and L.F.C. ; software, A.H. ([PERSON]); supervision, [PERSON] ([PERSON]); validation, [PERSON] ([PERSON]); visualization, A.H. ([PERSON]); writing--original draft, [PERSON] ([PERSON]); writing--review & editing. [PERSON]. ([PERSON]), L.F.C. and [PERSON]. ([PERSON]). All authors have read and agreed to the published version of the manuscript. The publication of this article was funded by Chemnitz University of Technology. Not applicable.