# A Novel Physics-Guided Neural Network for Predicting Fatigue Life of Materials
## 1 Introduction  
The fatigue failure of materials has always been the focus of research in the field of engineering. Fatigue failure is sudden and destructive. Unlike static failure, it may occur when its actual load is much lower than its yield load. In order to achieve a balance between safety and economy, it is necessary to predict the fatigue life of materials in the engineering field. In Europe, research on fatigue began in the early 19 th century. German mining engineer [PERSON] was the first to observe that the strength of metal materials operating under repeated loading is lower than the static strength of the materials. In 1854, [PERSON] was the first to coin the term \"fatigue\" to describe the phenomenon of metal cracking under repeated action at lower loads [1]. Many researchers have since studied fatigue in terms of the stress amplitude-life curve ([PERSON]), the influence of average stress on fatigue life ([PERSON], [PERSON], [PERSON]) [2; 3; 4], and [PERSON]'s equation (Basquin) [5]. These efforts have promoted the development of fatigue research. The traditional method for fatigue life prediction is the explicit method. One of the typical examples is the Basquin equation, which characterizes the relationship between fatigue life and load. Using the Basquin equation, only two fatigue performance parameters need to be determined to directly determine the fatigue life in combination with the load. However, it has the following limitations: 1. There are many factors that affect the fatigue life of materials, such as temperature, notch, corrosion, stress ratio, etc. These changes in the service environment will directly affect the correspondence between load and fatigue life. 2. The two fatigue performance parameters need to be obtained by the corresponding fatigue test, and the obtained parameters can only be used in the load environment corresponding to the fatigue test, which has high requirements for time andeconomic resources. Based on the above reasons, the traditional explicit model cannot meet the needs of the engineering field. Due to the rapid development of computer technology, machine learning technology has gradually played a very important role in the engineering field [6]. It is difficult to determine the fatigue life directly by the determined mathematical solution method, and the fatigue experiment usually has noise [7; 8; 9]. There may be errors in the measurement of experimental parameters [10]. Machine learning is a promising solution for similar fields. At present, there are many machine learning methods used in the prediction of fatigue life: [PERSON] et al. used the random forest method to predict the fatigue life of rubber under constant amplitude strain loads [11]. [PERSON] et al. predicted the fatigue life of laser cladding Ti-6 Al-4V alloys using the support vector regression method [12]. [PERSON] et al. successfully predicted the multiaxial fatigue life with different loading paths through a recurrent neural network [13]. Among them, the neural network method has been widely used in the field of fatigue life prediction due to its structural diversity. As a fully data-driven model [14], the above machine learning methods rely heavily on a sufficient number of training data [15], and the data extrapolation ability is poor [16]. Especially when the coverage of training samples is insufficient, its predictive ability will be greatly reduced [17]. Based on the above reasons, some scholars have tried to embed information into neural networks to improve their data extrapolation capabilities. [PERSON] et al. embedded the Stokes equation into the loss function of the neural network to predict the pressure, velocity and other parameters inside the fluid. In the process of learning, the network not only satisfies the error reduction of the training data, but also ensures that the prediction results conform to the Stokes equation [18]. In the field of fatigue life prediction, [PERSON] et al. proposed a physical probability-guided neural network.