## 3 Machine Learning Model  
Artificial neural networks (ANNs) have recently become a key method for analyzing and optimizing foamed bitumen bound asphalt mixtures. They can provide a useful approach to predict and to enhance the properties of the mixture materials. Many studies have noted that ANNs can effectively improve complex relationships between various input factors such as temperature, foam content, expansion ratio, and half-life, alongside outputs like Marshall Stability and ITS [26]. For instance, a back proportion or feedforward neural network with its hidden layers has been successfully employed to predict the characteristics of bitumen mixtures, resulting in reliable and accurate prediction equations [27]. Furthermore, the integration of ANNs with particle swarm optimization has improved foamed bitumen properties in cold recycling technology by enhancing prediction accuracy through the analysis of multiple variables, including temperature and water content [28]. Researchers have also advanced the prediction of mechanical properties in foamed bitumen bound asphalt pavements using ANNs, which aids in optimizing pavement design and in thoroughly understanding input-output dynamics [9; 29]. To obtain precise predictions and determine the optimal percentages of reclaimed asphalt pavement (RAP) and foamed bitumen content (FBC), various AI models have already been developed. The primary focus was on three main models: Random Forest (RF), Support Vector Regression (SVR), and Linear Regression. Support vector regression (SVR) is an effective machine learning technique for modeling and forecasting material behavior in pavement engineering, especially in the field of foamed bitumen bound asphalt mixtures. Its advantage lies in its ability to capture nonlinear relationships by transforming input data into a higher-dimensional one using nodes and functions. This capability is important to understanding the complex behaviors of asphalt materials. Research has indicated that SVR effectively predicts various performance properties of foamed bitumen bound asphalt mixtures, such as Marshall Stability and Flow, which are affected by many factors like bitumen content, foam expansion ratio, and temperature [30; 31]. This technique has confirmed prediction accuracy in comparison with traditional regression models, especially in situations of limited sample sizes, so reducing the risk of overfitting [30]. Notably, SVR has been successfully employed to forecast the performance of foamed bitumen bound asphalt mixtures used in cold recycling technology by providing accurate predictions for long-term pavement durability. Additional is SVR's capacity to deliver estimates of foamed bitumen behavior in different conditions and improve the optimization process in pavement material design [32]. Random forests (RF) have emerged as a machine learning approach for predicting the characteristics and performance of foamed bitumen bound asphalt mixtures. This technique creates numerous decision trees and aggregates their outputs, which leads it to be effective in handling high-dimensional data and showing nonlinear interactions between variables [33]. In applications related to foamed bitumen bound asphalt mixtures, RF models have efficiently predicted key metrics like Marshall Stability, Flow, and rutting resistance against different factors such as foam content, bitumen temperature, and water content [34; 35]. The strengths of RF are clear in its ability to manage inclusive and varied datasets, perform reliably across different sample sizes, and provide accurate predictions with minimizing the risk of overfitting, which especially takes place in traditional machine learning methods [35]. For example, RF has played an important role in enhancing the mix design of foamed asphalt by clarifying the interaction between mix components and pavement performance [8].