## 4 Conclusions  
The results of this study suggest that the following conclusions:  
* According to Tables 4 and 5, we can conclude that artificial neural networks are able to predict values of all the studied parameters of cutting, with MLP 3-3-5 which has low error backpropagation characteristics being the optimal neural network.
* The width of a kerf at the upper surface (WKU) and the width of a kerf at the lower surface (WKL) do not increase with a \(P\) higher than 300 W.
* Both AR and P do not have a significant effect on WHAZU and WHAZL.
* AR changes WKR only when \(P\) is lower than 300 W, thus AR has an effect on WKR only for low CO\({}_{2}\) laser powers.  
Figure 4: WKR vs. AR, P at 1.2\(\cdot\)10\({}^{-2}\) m\(\cdot\)s\({}^{-1}\).  
* The values of WKU for all the studied parameters of \(P\) and AR are statistically significantly higher than for WKL which is in contrast with the increased value of WHAZL vs. WHAZU at cca. 40% level.
* The values of WKR at a \(P\) higher than 200 W are cca. equal to 0.7 which is a very low value therefore higher powers lead to worse cutting quality so we can conclude that they are not appropriate for a cutting speed of 1.2\(\cdot\)10\({}^{-2}\) m\(\cdot\)s\({}^{-1}\).
* Generally, the value of \(P\) = 200 W improves the cutting quality in the terms of WKR values and therefore they are optimal for wood cutting at 1.2\(\cdot\)10\({}^{-2}\) m\(\cdot\)s\({}^{-1}\). The values of WKR at \(P\) = 200 W are higher than the values of this parameter at 100 and 150 W even if the cutting speed at optimization (1.2.10\({}^{-2}\) m\(\cdot\)s\({}^{-1}\)) is higher than at the measured dataset (max 0.9. 10\({}^{-2}\) m\(\cdot\)s\({}^{-1}\)).
* Prediction of the cutting conditions of spruce wood machined by CO\({}_{2}\) laser effects on cut characteristics, obtained by artificial neural network MLP 3-3-5, can be used for qualitative characterization of the cutting conditions in wooden technological processes.
* In our article, we predicted the effect of P and AR by constant value of \(\
u\) on the cut characteristics and therefore we used regression modelling using ANN in Statistica software. According to abovementioned parameters this showed a very good correlation, and a low sum of squares error, which for characterization of wood materials cutting is highly under the error level at which these properties are measured, which is in good agreement with other authors' results.
* In the next stage of research, we will focus on studying the cutting speed \(v\), the number of annual circles (AR) and the laser power \(P\) effect on all above-mentioned parameters, as it is very useful to compare the results with other approaches, which should be deep learning approaches, non-linear parametric fitting procedures and many others to optimize the accuracy of the prediction of cut characteristics.  
Conceptualization, I.R. and R.I.; methodology, R.I. and I.R.; software, I.R.; validation, I.R., R.I. and I.K.; formal analysis, I.K. and M.G. and A.J.; investigation, I.R., R.I. and I.K.; resources, I.K.; data curation, I.R. and R.I.; writing--original draft preparation, I.R.; writing--review and editing, R.I. and I.K.; visualization, A.J.; supervision, I.K.; project administration, I.K.; funding acquisition, I.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Slovak Research and Development Agency under the Contract no. APVV-20-0159 (80%) and by the VEGA Agency of the Ministry of Education, Science, Research, and Sport of the Slovak Republic and the Slovak Academy of Sciences Grant no. 1/0577/22 (20%).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.