## 4 Discussion
However, that feature does not occur if the total number of neurons is higher, see Figure 6, i.e., for 1000 or more of total neurons, the fluctuations are not so significant and the trend is not always preserved. For instance, in the best case, \"1024, 8192\", the relation is the opposite; for 200 epochs, the MSE is 0.00016, while for 800 epochs the MSE equals 0.00019. It should be emphasized that the overfitting effect may occur for a large number of epochs. Therefore, an ANN with a lower epoch number should be preferred when comparing two ANN configurations with similar errors. The verification of the values of the effective stiffnesses were also computed in Section 3.3 for selected cases, see Table 3. In the first example, the greatest error was equal to 3.11% and 1.44%, while the rest was not greater than 0.6%. In the second example, the greatest error was equal to 1.5%, while the rest was not greater than 0.7%. In the third example, the greatest error was equal to 2.9% and 1.41%, while the rest was not greater than 0.8%. In the fourth example, the greatest error was equal to 3.26%, 2.43% and 2.15% while the rest was not greater than 1.0%. In the fifth example, the greatest error was equal to 1.1% and 0.62%, while the rest was not greater than 0.51%. In the sixth example, the greatest error was equal to 1.38%, 0.78% and 0.76%, while the rest was not greater than 0.45%. Individual effective stiffnesses with high error values were not observed. As shown above, for random examples selected, the biggest error was 3.11%, which proves very good agreement between the value computed by trained ANN and the value computed due to homogenization algorithm [10]. Those magnitudes of values of error in homogenization computations are acceptable as shown in [12; 18]. Having a quick and reliable approximation of the RVE properties of prefabricated hollow-core slabs makes it possible to analyze the effect of changing the parameters on the individual mechanical properties of this complex structure. The example of such analysis was shown in this study, see Section 3.4. In Table 10 and Figure 7, the effect of changing the height of the prefabricated slab on its effective stiffnesses, i.e., compression/tension, bending and transversal shear stiffnesses was demonstrated. Other parameters of RVE were fixed. In Figure 7a, it may be observed that the influence on \(A_{11}\), \(A_{22}\), \(A_{12}\) and \(A_{33}\) is linear. For those properties, the maximal increase of the height, i.e., 33%, causes the increase of 69%, 49%, 74% and 61% of the effective stiffnesses, respectively. The influence is one and a half times greater, taking into account \(D_{11}\), \(D_{22}\), \(D_{12}\) and \(D_{33}\), the values are increased with 159%, 146%, 171% and 156% for 0.4 m slab height, respectively. The trends for \(D\) stiffnesses are slightly nonlinear, see Figure 7b. While considering the transversal shear stiffnesses, i.e., \(R_{44}\) and \(R_{55}\), the growths are linear, see Figure 7c. The percentage increases for 0.4 m slab height are 93% and 70%, respectively. The above analysis of five examples was derived from ANN computations which took less than 0.1 s.  
The ANN model built in the study gives the computational results in a very short time. The numerical homogenization for 50 models takes about 26 min, while for 200 models it is about 104 min. The ANN computations for 50 models last about 0.6 s, while for 200 modelsit lasts 0.75 s. The time saving while comparing the homogenization method and ANN computations is several thousand times. There are a few limitations of the study, namely, relatively simple measure for error was used for training the ANN. In the literature, there are a lot of other functions, which may reduce the probability of overfitting. Also, for finding the solution with lower MSE, the trial-and-error method was used. One can utilize a more elaborate method to determine the number of layers and neurons through solving formal optimization problem. However, it should be properly conditioned to avoid overfitting.