## 1 Introduction
### Deep Learning-Based Topology Optimization  
DL-based TO, by predicting the geometry through ANNs, aims to deliver optimized results in only a fraction of the time required by conventional optimization, by moving the computationally intensive part to the training algorithm, which executes only once. The trained ANN provides results which can be used directly, refined with conventional methods or adapted to the desired structure size. There have already been some attempts in this area. Some approaches [10; 11; 12; 13; 14; 15; 16] used an ANN or a generative adversarial network (GAN) [17] to map the boundary conditions directly to the desired optimized geometries. They, therefore, required many thousands of topology-optimized geometries as training data points for the ANN and achieved near-optimal results in terms of geometric similarity. [PERSON] et al. and [PERSON] et al. used some physical fields over the initial domain, such as strain energy density or von Mises stress, for the training of the neural network [18; 19]. [PERSON] et al. used an approach in which intermediate results of conventional TO are the basis for the training data points for the ANN, which is able to produce 3D geometries [20]. [PERSON] et al. used a data-driven approach, which is characterized by selecting the best data points for training [21]. [PERSON] et al. used a theory-driven approach in which two cases were trained and tested. In the first case, the direction of a single load could be changed. The second case had variable directions as well as the positions of the load [22]. A different approach was presented by [PERSON] and [PERSON], where the ANN does not generate the whole geometry but only a density value at given x and y coordinates. This method provides very good results at high resolution and is also applicable to the 3D case. A disadvantage is that the training must be repeated when the boundary conditions are modified [23]. [PERSON] and [PERSON] used DL to speed up conventional TO by [24] by using the results from some conventional TO iterations as input for the ANN. [PERSON] and [PERSON] accelerated conventional TO by utilizing surrogate models for forward and sensitivity calculations [25]. These approaches are indirect since some iterations are required. Although such DL-based TO procedures are able to perform the above-mentioned task of a fast and mostly direct generation of optimized geometries, the predictions undergo some restrictions. State-of-the-art procedures require the use of large number of optimized training data points. These training data points must be optimal to be suitable as training data. Depending on the optimization formulation, this may be not the case, as local minima and convergence problems may occur. A method that does not use optimized data is not subject to these restrictions. Since topology-optimized training data are used, and the generation of these data with conventional methods is very time consuming, the number of training data points that can be considered is limited. In the case of [10], 100,000 training data points were generated; this took about 200 h. Another 8 h were needed for training. This limitation affects the accuracy in the prediction of unknown geometries (i.e., geometries which were not used within the training) negatively. For those approaches that do not require optimized data, but require initial or intermediate results of conventional TO, the input data points must be available prior to training. Therefore, the aforementioned limitation persists. This paper investigates the possibility, which differs from the state-of-the-art methods, to train an ANN without the use of optimized or computationally prepared data. The generation of training data points and the training itself are merged in one single procedural step, also called online training. Unlike existing approaches, the ANN does not need to be re-trained if the boundary conditions are altered. This makes it possible to process a much larger amount of training data points for the training in a much shorter time.