## 4 Fatigue Life Modelling and Prediction in Hydrogen Environment  
Fatigue life prediction in hydrogen environments is very important, especially for metallic materials in engineering applications. Materials in hydrogen environments are susceptible to hydrogen embrittlement, which results in reduced mechanical properties, reduced ductility, and significantly shorter fatigue life. Therefore, fatigue life prediction can help engineers and scientists to assess the service life and safety of materials in hydrogen environments. Existing fatigue life prediction models for hydrogen environments are broadly classified into four categories:  
The first one is empirical models [20; 21; 22; 23; 24; 25], which are usually based on experimental data and statistical analyses, and describe the fatigue life of materials under different conditions by fitting curves or equations. Common empirical models include [PERSON]'s equation, [PERSON]'s equation, etc. [23; 24; 25]. These models have the advantage of simplicity and ease of use, but may suffer from low accuracy in predicting complex situations. The second category is physical models [26; 27; 28; 29; 30; 31], which are based on the understanding of the microstructure and crack behaviour of the material and use mathematical equations to describe the crack growth process and consider the effect of hydrogen in the material. These models usually require an in-depth understanding of materials science and mechanics and can provide more accurate predictions, but can be more complex to build and solve. The third category is numerical simulations [28; 32; 33]. This category encompasses various numerical methods, including the finite element method (FEM) as a specific case. Numerical simulations can model the stress field and cracking behaviour of materials by discretizing the structure into finite elements and solving mechanical equations for each element. In addition to FEM, phase-field modelling can be applied to simulate the evolution of microstructural features like cracks and phase boundaries in a diffuse manner, enabling detailed insights into fracture and phase transformation processes. Other numerical methods, such as molecular dynamics, can also be explored to provide insights into material behaviour at the atomic level. These simulations can handle complex geometries and loading conditions, offering detailed information on stress distribution and phase evolution but requiring significant computational resources and specialised software. The fourth category is surrogate modelling such as machine learning methods [34; 35; 36; 37; 38; 39]. Machine learning methods use large amounts of experimental data and features to train models to predict the fatigue life of materials. Common machine learning algorithms include regression analysis, support vector machines and neural networks. These methodscan handle complex nonlinear relationships and high-dimensional features, but require sufficient data volume and proper feature selection. Research works for fatigue life modelling in hydrogen environments have been summarised in Tables 1 and 2. The current fatigue life prediction models for hydrogen environments still suffer from several major shortcomings: lack of comprehensive consideration of hydrogen-induced damage mechanisms, insufficient accuracy of model parameters, limited applicability, insufficient validation, and difficulty in considering the interaction of multiple factors. To solve these problems, it is essential to gain an in-depth understanding of how hydrogen affects the microstructure and mechanical properties of materials. Additionally, improving model parameter accuracy, enhancing model versatility, validating reliability, and accounting for complex interactions among multiple factors are necessary steps. These efforts aim to provide more reliable support and guidance for applying hydrogen technology in the engineering field. \begin{table}