## 2 Materials and Methods
### Feature Engineering  
After completing the data preprocessing, new features were extracted from the original ones to provide additional information not directly available in the initial feature set. The carbon-to-nitrogen ratio for each day was calculated and added as a new feature. Next,based on our knowledge of the process, the biomass growth rate, \(\mu\), was calculated using Equation (1), where \(X_{v}\) represents the biomass concentration at time \(t\), and \(X_{v_{0}}\) represents the initial biomass concentration. \[X_{v}=X_{v_{0}}\times e^{\mu t} \tag{1}\]  
Glucose and nitrogen consumption rates were calculated by subtracting the final concentration from the initial concentration (day 0) and then dividing by the total duration of the experiment. The biomass/substrate yield was calculated by dividing the biomass concentration at the end of the experiment by the substrate consumption throughout the days. Moreover, the specific rates of nitrogen and glucose consumption were also calculated using Equation (2). In Equation (2), \(S\) represents the glucose concentration when calculating the glucose consumption rate and nitrogen when calculating the nitrogen consumption rate. \[q_{S}=\frac{1}{X_{v}}\times\frac{dS}{dt} \tag{2}\]  
Finally, the increases or decreases that the substrate, nitrogen, MEL, or lipid concentration experienced between each day (Equation (3)) were also added as new features. \[\Delta X_{i}=X_{i}-X_{i-1} \tag{3}\]  
where \(\Delta X_{i}\) represents the change (increase or decrease) in the concentration of the variable \(X\) (e.g., substrate, nitrogen) on day \(i\), \(X_{i}\) represents the concentration of the variable on the current day (\(i\)), and \(X_{i-1}\) represents the concentration of the variable on the previous day \(i-1\). At the end of the feature extraction process, the final dataset was composed of 47 samples and 74 features. Feature selection methods were also applied to the dataset to ensure that only relevant information was provided to the models and to assess which features would have the greatest impact and be most relevant to predicting the MEL concentration. Five different feature selection methods were tested, therefore creating five different feature subsets. A principal component analysis (PCA) was the first method explored for feature selection. It creates several principal components, where each component is a linear combination of the original features. To reduce the dimensionality of the dataset, the number of principal components was first selected to ensure that they explained 90% of the total variance. Then, the mean contribution of each original feature across all of the selected principal components was calculated. Features with an overall negative mean contribution were discarded, as they pn average contributed inversely to the variance captured by the principal components that explained 90% of the variance [32]. The dimensionality was also reduced using the analysis of variance (ANOVA) method. In the context of feature selection, an ANOVA is used to rank the features by calculating the ratio of the variances between and within groups [33; 34]. Then, the same number of features previously obtained from the PCA was selected from the feature ranking. The Least Absolute Shrinkage and Selection Operator (LASSO) technique was also used for feature reduction. LASSO is a regression method that incorporates a penalty term, known as L1 regularization. The L1 regularization term is the sum of the absolute values of the regression coefficients, multiplied by a tuning parameter. LASSO works by simultaneously finding the coefficient values that minimize the sum of the squared differences between the predicted and actual values (the residual sum of squares) and minimizing the L1 regularization term. As a result, LASSO shrinks some coefficientstowards zero, which can then be used to reduce the feature set by eliminating those with a coefficient of zero [35,36].