## 2 Materials and Methods
### Experimental Setup  
The experiments were performed with MATLAB R2023b using the Statistics and Machine Learning Toolbox (MATLAB 23.2, R2023b) for custom training experiments for machine learning and Bayesian optimization. In addition, the Parallel Computing Toolbox (MATLAB 23.2, R2023b) facilitated the simultaneous execution of multiple trials. The MATLAB Experiment Manager was crucial for planning and running experiments to train and compare the neural network models. In the Experiment Manager, a set of hyperparameters were explored using Bayesian optimization, with each experiment generating a set of results for each run. These results comprised 1500 trials, each representing a distinct combination of hyperparameters. The pseudocode in Appendix A outlines the process for training a regression neural network model, tuning the hyperparameters, and computing associated metrics in the experimental settings. The parameters optimized during the modeling process are 'Activations', 'Lambda', 'LayerSizes', and 'Standardize'. These parameters are options for the optimization of hyperparameters in connection with the fitting of a neural network regression model (_fitnet_). The specific functions and effects of each parameter are explained below:  
1. _Activations_: This parameter refers to the choice of activation functions used in the neural network layers. Activation functions introduce non-linearity into the neural network and allow it to learn complex relationships in the data. 2. _Lambda_: This parameter represents the strength of regularization, often referred to as \(\lambda\) (lambda), which penalizes significant coefficients in the neural network model. Regularization helps prevent overfitting by discouraging overly complex models. Figure 2: Training and test datasets’ split distribution. _LayerSizes_: This parameter refers to the size (number of neurons) of the hidden layers in the neural network. The selection of appropriate layer sizes is crucial for the balance between model complexity and performance. * _Standardize_: This parameter specifies whether or not each numeric predictor variable should be standardized before fitting the neural network. When standardizing, the predictor variables are scaled to have a mean of zero and a unit standard deviation. This can improve convergence and performance, especially if the predictors have different scales. There are numerous normalization methods, including statistical normalization, standardization, sigmoidal normalization, and others. In this study, standardization is used because it results in consistent variances in the features and normalizes the input features to the same range [48]. In hyperparameter optimization, the goal is to find the combination of these parameters that minimizes the cross-validation loss and, thus, optimizes the performance of the neural network model for the task at hand [29]. Five distinct experiments with different hyperparameter settings were conducted for the hyperparameter optimization process. Using the BO methods of hyperparameter optimization and cross-validation schemes, different combinations of hyperparameters were investigated in the experiments, including the number of layers, activation functions, standardization techniques, regularization parameters and layer sizes. Systematically varying these parameters and performing 5-fold and 10-fold cross-validation experiments, the study aimed to identify optimal model configurations that balance model complexity and generalizability, thereby improving the accuracy of predicting hardenability. The experiments were run for 1500 trials, and validation RMSE was recorded as the performance metric. 1. Experiment 1 (10-fold CV): NumLayers [1; 2], Activations ['relu', 'tanh','sigmoid', 'none'], Standardize ['true', 'false'], lambda [1.9172 \(\times\) 10\({}^{-9}\), 0.1], Layer 1 [1; 300] and Layer 2 [1; 300]. 2.