## 2 Materials and Methods
### Machine Learning Techniques  
Different machine learning techniques were employed to forecast the MEL concentrations at the end of days 4 and 7. This study used three supervised ML algorithms: a support vector machine, random forest, and neural network. These models were chosen for different reasons. Random forest models are easy to implement and allow the path back to the output to be tracked, support vector machines are very efficient in high-dimensional spaces, and neural networks can model the complex, non-linear relationships in data. Additionally, these three models are among the most commonly applied machine learning techniques in bioprocess forecasting studies [20,22,23,24]. Real-world data often exhibit non-linear separability, making it challenging to distinguish between classes in the original feature space and to determine the separation surface effectively. To address this challenge, kernel functions are employed to transform the data into a higher-dimensional feature space where the classes become more easily separable. Among the several existing kernels, the most common ones are linear, polynomial, the radial basis function (RBF), and sigmoid. A support vector machine is an algorithm used for both classification and regression tasks. The SVM uses this kernel-based mapping to transform the data into a higher-dimensional space, where it then searches for the optimal hyperplane that can separate the data. The construction of the hyperplane is mainly dependent on the support vectors, which are created through data points from the training set and support the margins of the hyperplane. The choice of kernel function is a key hyperparameter in the SVM since it allows the model to operate in a high-dimensional feature space without explicitly calculating the coordinates in that space. This is essential because high-dimensional spaces are often too large to compute directly, making the calculations slow or even impractical for large datasets. A detailed description of the method can be found in [PERSON], 2020 [40]. The random forest model was also used in this study. Random forest is an ensemble learning method, a combination of several inducers, more specifically decision trees (DTs). Each DT in the forest is a simple model that has low accuracy individually since it only uses a subset of the features. By aggregating the DTs, using averaging for regression or majority voting for classification, the RF algorithm can construct complex decision surfaces that effectively separate the classes. One of the advantages of RF is its ability to achieve a high accuracy even with limited data relative to the number of features, as it utilizesbootstrap sampling to generate diverse training subsets for each tree. More information about this model is presented in [PERSON], 2012 [21]. Finally, predictions were also made using a feed-forward neural network (NN). Briefly, an NN is divided into three parts: an input layer, hidden layers, and an output layer. NN algorithms are inspired by the neural networks present in the human brain, where an external stimulus is received and propagated by a neural network connected by synapses that process the information and return a final command. In this approach, the input data are provided to the algorithm, which will activate certain nodes (or neurons) in the input layer, which will, in turn, activate other nodes in the hidden layers through the weight connections associated with a bias. These interactions generate an output based on the connections from the input layer through the hidden layers. Training data must be provided to the algorithm so it can learn the weights that connect the various neurons, enabling accurate predictions. The weight learning process is carried out through backpropagation, which is a cost function minimization through gradient descent. When test data are provided to the network, it should be able to predict these new and unseen entities based on the learning from the training set [41].