## 3 Results and Discussion
### Comparison of the RSM and ANN Models  
The performance of these models is analyzed statistically with the root mean square error (\(RMSE\)), determination coefficient (\(R^{2}\)), and the absolute average deviation (\(AAD\)), based on the following equations: [34]  
\[RMSE=\sqrt{\frac{1}{n}{\sum\limits_{i=1}^{n}}{\left({F_{i}-A_{i}}\right)^{2}}} \tag{3}\]  
\[R^{2}=\frac{{\left({\sum\limits_{i=1}^{n}}{\left({A_{i}-\overline{A_{i}}} \right)\left({F_{i}-\overline{F_{i}}}\right)}\right)^{2}}}{{\sum\limits_{i=1}^ {n}}{\left({A_{i}-\overline{A_{i}}}\right)^{2}}{\left({F_{i}-\overline{F_{i}}} \right)^{2}}} \tag{4}\]  
\[AAD=\left|{\left({\frac{1}{n}{\sum\limits_{i=1}^{n}}{\left({\frac{{F_{i}-A_{i}} }{{A_{i}}}}\right)}}\right)}\right|\times 100 \tag{5}\]  
where \(n\) is the number of points, \(F_{i}\) is the value obtained from the forecast with the RSM or ANN model, \(A_{i}\) is the value obtained experimentally, and \(\overline{F_{i}}\) indicates the average of the equation located under the symbol.  
The values forecasted by both models are close to experimental values, but the determination coefficient value closer to 1 corresponds to the ANN model, which indicates a better fit of the ANN against the one presented by the RSM. Moreover, the \(RMSE\) and the \(ADD\) values are smaller in the ANN prediction. The results of the error calculation for both models are shown in Table 4.  
Figure 6: The surface of the ANN with the best performance.  
Figure 7: Contour graph of the ANN with the best performance.  
The R-squared values obtained for the RSM and ANN models are 0.8284 and 0.9952, respectively. The ANN represents 99.52% of the data. The closest model is the ANN developed for modeling the yielding L-methioninease from _Trichoderma harzianum_ with a determination coefficient (R\({}^{2}\)) equal to 0.9950 [16]. The RSM model proposed to represent the mass production of _Trichoderma Brev T069_ shows an R\({}^{2}\) equal to 0.9763 [14], and the authors did not propose an ANN model.  
The RSM and ANN techniques have been used to model biotechnology processes satisfactorily [35; 36]. Similarly to the results presented in this paper, other publications have proven that ANNs denote better performance than RSM models. For example. in the study carried out by the authors of [30], they observed a better modeling ability of the ANN over the modeling performed with RSM. The strength of the ANN for making generalizations of the modeled data could be due to its ability to model nonlinear systems, unlike RSM, which is limited to polynomial models.  
The main importance of using ANN in biologically driven systems is that they do not require a full understanding of the relationships between all the factors that influence the outcome. Moreover, an ANN can represent different signal characteristics from the input information, even implicitly combining factors with no \"a priori\" well-defined relationship [37]. In addition, one of the primary strengths of ANNs is their remarkable ability to learn patterns and relationships from data and carry out functions such as classification, generalization, and prediction [38; 39].  
Thus, the variables involved in the process of conidiospore production can be modeled and analyzed through ANNs. The ANN with the best performance is used for obtaining the best conditions to maximize the number of conidiospores, and it will increase the production of conidiospores under optimal conditions.