## 3 Results and Discussion  
Before applying the ML workflow (Figure 1), data characterization was carried out. Firstly, the MEL concentrations on days 4 and 7 are represented in Figure 2 and show no clear pattern between the two time points. However, when [PERSON]'s correlation was calculated for these two variables, a value of 0.78 was obtained, revealing a strong positive correlation. [PERSON]'s test, which measures the strength and direction of a monotonic relation, was also used, revealing a correlation coefficient of 0.82, further reinforcing the [PERSON]'s correlation results. Given the established relationship between the two variables, it is reasonable to hypothesize that predicting the MEL concentration on day 4 could serve as an early indicator of the outcome on day 7. This baseline could help forecast whether a particular shake flask would achieve the desired MEL concentration, allowing for a more informed decision on whether to proceed with the fermentation process or not. As previously stated, three different machine learning models were trained to predict the MEL concentration at the end of days 4 and 7 using 37 samples. Therefore, 10 samples were kept aside for testing in a different file to avoid data leakage, corresponding to a train-test split of 80/20. The testing set was chosen at random so as not to introduce any human bias. This split ensures that the model is trained on most of the data while still being tested on a significant portion that remains unseen during training. Then, from the training set, 7 samples were chosen to serve as the validation set, while the remaining 30 samples were used to train the models. This validation set was used to assess the performance of the model on the training set. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Hyperparameter** & **Day 4** & **Day 7** \\ \hline \multirow{8}{*}{Random Forest} & Number of estimators & 10 & 1 \\  & Criterion & Absolute error & Squared error \\  & Maximum depth & None & None \\  & Minimum sample split & 3 & 3 \\  & Maximum features & Sqrt & Sqrt \\  & Bootstrap & True & True \\ \hline \multirow{4}{*}{Support Vector Machine} & Kernel & RBF & Polynomial \\  & Epsilon & 0.001 & 0.001 \\  & Gamma & 1 & 0.001 \\  & C & 0.1 & 75 \\ \hline \multirow{4}{*}{Neural Network} & Number of layers and & [64; 32; 16] & [128; 64] \\  & neurons & & \\ \cline{1-1}  & Loss function & MSE & MSE \\ \cline{1-1}  & Output layer & 1 & 4 \\ \cline{1-1}  & Batch size & 8 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyperparamaters selected for each model for forecasting the concentration of MELs on day 4 and day 7 of the process. As described in Section 2.4, all of the models were trained during the hyperparameter optimization step. Although the models obtained low errors when asked to predict the validation set, it was important to check for their ability to generalize over unseen data. It is also important to note that the dataset used was relatively small, and a larger dataset could further enhance the accuracy of the predictions. Table 2 shows the MSE obtained for each model using each subset of the features for day 4, and in Table 3, the experimental values, the predicted values, and the prediction errors are presented. The same information for the day 7 predictions can be found in Tables 4 and 5. Overall, the predictions for day 4 were more successful than those for day 7, which was not expected since the features used for the forecasting of day 4 included only the first two days of fermentation. It is also worth noting that the models benefited from the feature selection process since a lower MSE was achieved by each model when feature reduction techniques were applied.