# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 2 Materials and Methods
### Methods
#### 2.2.5 Data-Driven Predictions of Rheological Parameters  
The rheological characteristics of the extracted binders were predicted from the mix data (e.g., total AC%, ABR by RAP%, ABR by RAS%, mix type, and mix age in years), chemical indices, and residue thermal percentage. This was accomplished using machine learning algorithms implemented in Python (version 3.13), both linear and nonlinear models. Feature importance plots and heat correlation maps were generated to identify the most critical factors in these models. Different statistical metrics were used to quantify the accuracy of the model predictions, including the coefficient of determination (R2), Pearson's correlation coefficient (R), ratio of standard error to standard deviation (Se/Sy), mean residual, standard deviation (STD) of residual, and root mean square error (RMSE).  
During model selection, different machine learning methods were reviewed, including support vector regression (SVR), artificial neural networks (ANN), and extreme gradient boosting (XGBoost). However, the RF was selected because of its better predictive power, inbuilt resistance to overfitting, and excellent interpretability in the presence of limited data or strongly nonlinear relations being modeled. In addition, RF is more practical and easier to explain than SVR or ANN, which require much more careful tuning, and then there is XGBoost, an actual overfitting risk [48, 49, 50].  
In Python, an RF regressor is an ensemble learning method that creates and trains several decision trees on different sub-samples of data and features. The trees learn in parallel and independently of one another as to whether they will provide a systematic pattern by splitting the data according to a threshold value along the respective features. The final prediction for regression tasks provided by the RF is the average of all the tree outputs. This is because the RF regressor has many trees of various structures, with different decisions that result in a model that is not a linear equation defining the entire model. There are essentially two major parts to the RF process: training and testing the model. Training the model implies that the algorithms learn from the training data. The data are used to create decision trees, and their split is then refined to minimize the prediction error [48, 49, 50].  
RF models were produced using the Python library (scikit-learn). A systematic search of the hyperparameters was conducted to select the parameters that optimized performance from cross-validation. The search space included 100, 200, and 300 trees using the n_estimators parameter. The maximum depths were none, 10, 20, and 30, specified by the max_depth parameter. The number of samples needed to split an internal node was 2, 5, and 10, as highlighted by the min_samples_split parameter. The number of samples at a leaf node was 1, 2, and 4, as specified by the min_samples_leaf parameter. The search was carried out using GridSearchCV to make a search and then determine the best parameters to use, dependent on cross-validation performance. To decrease potential sampling bias, the dataset was randomly shuffled and split, with scikit-learn's internal functions, into an 80:20 training and test set to provide a balanced training and unbiased evaluation.