# Ultra-High-Cycle Fatigue Life Prediction of Metallic Materials Based on Machine Learning
## 1 Introduction  
Metal structures are generally subjected to cyclic loading during their service periods; thus, fatigue mechanisms trigger the nucleation of microcracks, crack expansion, and eventually, the complete failure of structures [1]. Due to the demand for environmental protection, metal structures should serve longer than ever, indicating that their fatigue life should exceed \(10^{7}\) cycles (ultra-high-cycle fatigue life regime) [2]. Fatigue tests are most commonly used to predict the ultra-high-cycle fatigue life of metallic materials; however, fatigue tests are costly and time-consuming. Extensive research has been carried out to predict the ultra-high-cycle fatigue life of metallic materials more quickly and accurately [3; 4; 5]. Research on the fatigue life prediction of metallic materials can be divided into two main directions: physical models and data-driven models [6]. Physical models perform fatigue failure analysis and life prediction based on surface integrity factors, such as residual stress, surface roughness, internal defects, and grain size. [PERSON] et al. [7] improved the Coffin-Mansarinegon model to increase fatigue life prediction accuracy. [PERSON] et al. [8] developed a fatigue life prediction model for surface carburized steel based on the definition of microstructures and the critical surface theory. [PERSON] et al. [9] proposed a fatigue life prediction model using the concept of energy dissipation threshold as a failure criterion within the framework of thermodynamics. [PERSON] et al. [10] adopted the small crack theory to predict the fatigue life of two aluminum alloys and one steel alloy under different load histories. Most physical life prediction models have been developed based on fatigue damage theories, such as linear damage rules, nonlinear damage curves, two-stage linearization approach, crack growth concept, continuum damage mechanics, and energy-based theories [11]. Physical models can predict the fatigue life of metal partsto a certain extent; however, due to the disadvantages of the imperfect fatigue damage accumulation theory and the requirement of numerous model parameters, they cannot be easily used in practical engineering applications. Data-driven models determine the relationship between the input and output of a given phenomenon based on available data [12]. With the development of artificial intelligence, machine learning (ML) has created more opportunities for data-driven models. [PERSON] et al. [13] proposed a damage mechanics-based machine learning framework for the data-driven fatigue life prediction of titanium alloys. [PERSON] et al. [14] used a support vector regression (SVR) algorithm to develop a fatigue life prediction model by post mortem fractography analysis. [PERSON] et al. [15] used a BP neural network to predict the VHCF life of centrifugal impeller blades. [PERSON] et al. [16] applied a neuro-fuzzy-based machine learning approach to predict the high-cycle fatigue life of laser powder bed-fused 316 L stainless steel. [PERSON] et al. [17] explored the use of ML to predict the microstructural sensitivity of three-dimensional (3D) crack surfaces in polycrystalline alloys. [PERSON] et al. [18] investigated the relationship between the fatigue crack growth rate (da/dN) and the stress intensity factor range (\(\Delta\)K) by a machine learning model and reported that the application of machine learning to fatigue life prediction could be feasible. However, current data-driven fatigue life prediction models have the disadvantage of difficult access to input parameters and single application scenarios. For example, [PERSON] et al. [14] used material microscopic properties as input parameters, which were difficult to be obtained and very expensive, to develop fatigue life prediction models. Thus, it is necessary to find a fatigue life prediction model with simple input parameters.