## 5 Conclusions  
In the conducted research, the GPSR algorithm with RHS and five-fold CV was used to obtain a system of robust SEs for the estimation of the interaction locations in Super Cryogenic Matter Search detectors. The results of the investigation showed that:  
* Using the GPSR algorithm, it was possible to obtain SEs (mathematical equations) that can estimate the interaction locations in Super Cryogenic Matter Search detectors with high accuracy. * Using a 5-CV process, the robust system of the five SEs has a more accurate estimation when compared to the estimation of only one SE. The RHS method proved to be very useful in finding the combination of the quality hyperparameters where the highest accuracy was achieved. From all the results, the best three cases of the SEs were selected and evaluated on the test set. The highest values of \(\overline{R^{2}}\pm\sigma(R^{2})\), \(\overline{MAE}\pm\sigma(MAE)\), \(\overline{RMSE}\pm\sigma(RMSE)\) were achieved in Case 1 and are equal to \(0.9876\pm 0.0048\), \(1.0096\pm 0.1215\), \(1.5506\pm 0.3050\). * From the obtained results, three cases were selected based on the final mean \(R^{2}\) score. From these cases, the SEs that achieved the highest estimation performance were selected as the main elements of the custom set of SEs. The results of the customized solution obtained on the entire dataset were equal to \(0.991087\pm 0.001291\), \(0.878362\pm 0.063662\), and \(1.326449\pm 0.100901\), respectively. The final evaluation of these equations on the entire dataset showed that this system had slightly better performance when compared to Cases 1, 2, and 3. * Unfortunately, the custom set of SEs required all 19 input variables to compute the output. However, if only Equation (7) was used, the highest estimation accuracy could be achieved, and to compute the output, only seven input variables were required. The proposed approach presented in this paper showed that using a simple GPSR algorithm with RHS and the 5-CV on low-end computer hardware can produce better results than the complex CNN architecture presented in [13]. The benefit of using the proposed approach is that the SEs were easily used, easy to comprehend, and require fewer computational resources than complex CNN architectures. The main problem of the proposed approach is the initial definition of the GPSR hyperparameter ranges in the RHS method. The ranges are not unique and depend on the investigation, so each time, it has to be tuned from scratch. Depending on the dataset, the population size, number of generations, and tournament selection have to be defined. The larger the dataset size, the smaller the population, number of generations, and tournament selection size values are. Besides those hyperparameters, the Pcoef has to be defined, and this parameter is the most-sensitive one. A small increase/decrease of this value can result in a fast increase/decrease in the length of the population members. The other important factor that influences the hyperparameter ranges is the computational resources on which the GPSR algorithm with the RHS method is executed. Future work will be focused on synthetically enlarging the dataset size to see if the estimation accuracy could be improved. Besides that, other ML methods will be investigated, especially ensemble methods, with the idea of improving the performance metric values as much as possible. Conceptualization, N.A. and S.B.S. ; methodology, Z.C. ; software, N.A. and M.G. ; validation, N.A., S.B.S. and M.G. ; formal analysis, N.A., S.B.S. and M.G. ; investigation, N.A., S.B.S. and M.G. ; resources, N.A., M.G. and Z.C. ; data curation, N.A., M.G. and Z.C. ; writing--original draft preparation, N.A., S.B.S. and M.G. ; writing--review and editing, N.A., S.B.S. and M.G. ; visualization, N.A., S.B.S. and M.G. ; supervision, N.A. and Z.C. ; project administration, Z.C. ; funding acquisition, Z.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.