## 3 Results and Discussion
### Neural Net Fitting Turbidity Prediction Model  
The results of the training to predict turbidity in wines with Neural Net Fitting revealed that the Levenberg-Marquardt (LM) and Bayesian Regularization (BR) learning algorithms presented better performance with an average representativeness of 0.96, as opposed to the Scaled Conjugated Gradient (SCG) algorithm, which presented an average representativeness of 0.85 for the system under study (Table 2). Considering the maximization of R\({}^{2}\), the neural network trained with the Levenberg-Marquardt algorithm with 25 neurons in the hidden layer was selected, which presents an R\({}^{2}\) of 0.988. A similar value was obtained in other investigations that have trained neural networks with the same algorithm but in different disciplines. In addition, it also presented some of the lowest values for MSE, RNSME, and AIC, demonstrating the feasibility of the supervised learning process for estimating turbidity. The actual versus estimated curve (Figure 2) also displays the efficiency of the neural network model observing a good fit between predicted and experimental values, as mentioned by [PERSON] et al. [30] and [PERSON] et al. [38], which is also explained for the upper value of R\({}^{2}\), justifying the selection. The metrics and the selected algorithm indicate that the model is quite robust because it updates the weight and bias values at the culmination of each epoch, as stated by [PERSON] et al. [39]. In addition, since it combines the gradient descent method and the Gauss-Newton method, it becomes an efficient optimization tool that reduces the sum of squared errors [40]. Different studies suggest that the Levenberg-Marquardt algorithm and its variations enhance ANN performance by increasing speed, accuracy, and success while preventing over-fitting, which supports the result of this research [41; 42; 43]. [PERSON] et al. [24] also selected this algorithm to apply and control the grape fermentation process because it is well-suited for cases with fewer neuron connections. This algorithm is known for its efficiency in training neural networks and is particularly effective when dealing with smaller networks. Additionally, the Levenberg-Marquardt algorithm is commonly used for nonlinear optimization problems, making it a suitable choice for training ANNs in scenarios where complex relationships need to be modelled and learned, like the system studied in the present research. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Node** & \multicolumn{4}{c}{**LM**} & \multicolumn{4}{c}{**BR**} & \multicolumn{4}{c}{**SCG**} \\ \cline{2-13}
**Number** & **R\({}^{2}\)** & **MSE** & **NRSME** & **AIC** & **R\({}^{2}\)** & **MSE** & **NRSME** & **AIC** & **R\({}^{2}\)** & **MSE** & **NRSME** & **AIC** \\ \hline  
\hline \hline \end{tabular} \({}^{1}\) Best Levenberg-Marquardt performance model. \({}^{2}\) Best Bayesian Regularization performance model. \({}^{3}\) Best Scaled Conjugated Gradient performance model.  
\end{table} 
Table 2: Neural Net Fitting performance metrics. ANN has been demonstrated to be a suitable technique when wine prediction is needed; [PERSON] et al. found that ANN can predict the age of wine with an average absolute percentage deviation below 1% [44]. Support Vector Machines (SVM) and random forest models were compared in the study, but the random forest model with one tree and the ANN model with a logistic function in the output neuron demonstrate accurate predictions of aging time values. The study highlights the effectiveness of computational models in predicting the aging time of red wines, offering valuable insights for quality control and certification in the wine industry. [PERSON] et al. found that ANNs can predict valuable properties of wine and reveal different wine classes based on total phenolic, flavonoid, anthocyanin, and tannin contents [45]; according to [PERSON] et al., ANNs have been used to classify and predict wine process conditions in wine technology [46].