## 1 Introduction  
Crack propagation in materials is a critical phenomenon that can lead to structural failure and compromise the integrity and safety of various engineering applications. Understanding and predicting crack propagation is crucial for the design and maintenance of durable and reliable structures. Traditional approaches for predicting crack propagation involve complex mathematical models and empirical equations, which often have limitations in capturing the intricate nature of crack behavior under different conditions [1, 2]. Crack propagation in materials involves complex and nonlinear behavior influenced by factors, such as material properties, loading conditions, and environmental elements. Traditional methods struggle to capture the complex relationships and dynamics involved in crack growth. Conversely, machine learning models excel at identifying complex patterns and nonlinear relationships within data, making them well-suited for modeling crack propagation processes. Traditional methods often rely on simplified assumptions and limited representations of the factors influencing crack propagation, leading to inaccuracies. In contrast, machine learning models can incorporate a broader range of factors, including material properties, loading conditions, temperature variations, and more. By training on extensive datasets that encompass diverse conditions and parameters, machine learning models can learn the intricate relationships between these factors and crack propagation, enabling more accurate predictions. Additionally, traditional methods lack generalization capabilities, meaning they struggle to predict crack propagation in materials or loading conditions that differ from those used during model development. On the other hand, machine learning models can generalize well to new and unseen scenarios, provided they are trained on diverse and representative datasets. This ability enables machine learning models to make accurate predictions for various materials, loading conditions, and temperature ranges, enhancing their applicability and reliability [3; 4]. The utilization of machine learning models empowers researchers to surpass the limitations of traditional methods when it comes to predicting crack propagation. These models provide improved capabilities in capturing intricate behaviors, integrating a wider array of influencing factors, leveraging extensive and diverse datasets, and adapting to new scenarios [1; 2; 5; 6; 7; 8; 9; 10]. As a result, machine learning-based approaches possess significant potential for advancing our comprehension of crack propagation and enhancing the design and dependability of structures and materials. Previous studies have utilized machine learning techniques for crack prediction in different materials. For instance, [PERSON]. [11] employed Random Forest Regressor to predict crack propagation in composite materials under various loading conditions. The study demonstrated that the model accurately captured crack behavior and showed improved performance compared to traditional analytical methods. Support Vector Regression (SVR) has also been applied for crack propagation prediction. [PERSON]. [12] utilized SVR to predict crack growth in metallic materials subjected to cyclic loading. Their results indicated that the SVR model achieved good accuracy in predicting the crack growth rate and exhibited better performance than conventional regression methods. Gradient Boosting Regressor has shown promise in crack propagation prediction as well. Ref. [13] employed this model to predict crack growth in composite material under different environmental temperatures. Their findings indicated that the Gradient Boosting Regressor achieved high prediction accuracy and outperformed other regression models, such as Random Forest and Support Vector Regression. Ridge, Lasso, and K-Nearest Neighbors are also commonly used models in machine learning applications.