PSI - Issue 79

Henrik Petersson et al. / Procedia Structural Integrity 79 (2026) 298–305

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FE-based modelling is severely limited by the time-consuming task of recalibrating constitutive models and fatigue models when new experimental data become available. Instead, artificial intelligence (AI) models o ff ers a path past these limitations while remaining grounded in reality via physics informed neural networks (PINN). This way, physical knowledge is integrated into the data-driven approaches. Today, machine learning has become an important role in many research areas, even in the field of fatigue. Model compression techniques within the AI domain was studied by Dantas et al. (2024) and the di ffi culties of training such algorithms by Glorot et al. (2010). Neural networks have been used for fatigue life predictions, where the input varies such as Young’s modulus, tensile strength, toughness, hardness, volume fraction, etc. Some recent work includes Gbagba et al. (2023), which investigated di ff erent classes of AI algorithms for predicting the fatigue life of welded components, or the comprehensive study on fatigue strength by Quraishy et al. (2025), which uses 3612 data points. Zhang et al. (2021) proposed a general fatigue life prediction method for components that are subjected to conditions that results in creep fatigue. For cases with small amount of data, the majority of the AI algorithms are lacking robustness and conver gence. By integrating the physical knowledge into the data-driven approach a PINN can provide the way forward for small data sets. The PINN concept was recently introduced by Raissi et al. (2019), and has been explored in the field of fatigue prediction and constitutive modelling. Work carried out by Wang et al. (2023), Yang et al. (2024) and Zhou et al. (2025) shows how PINN can be used for predicting the fatigue life. Bartosˇa´k et al. (2025), Halamka et al. (2023) and He et al. (2023) used PINN to predict the fatigue life under multiaxial loading. Solving one-dimensional problem in solid mechanics via PINN was done by Haghighat et al. (2021), while Singh et al. (2024) expanded the approach to transfer learning and surrogate models. Chen et al. (2023) demonstrated an approach for predicting the fatigue life using a small quantity of samples. The aim of the current work is to utilize AI algorithms to produce material models predicting fatigue life based on known stress and strain states, where the algorithms rely on limited amount of experimental data. The work also explores variable safety factors of fatigue models, which depend on the experimental data used during the training process. A further aim is to replace analytical modelling by AI algorithms, instead of the manually work needed to create these fatigue models. The idea is to create a model that predicts the fatigue life with stress amplitude as input using a PINN, and to model the prediction error in such a way that the resulting probability interval reflects the expected variability of the experimental data. Lets consider the following equation that describes the fatigue life, N f , in number of cycles, N f = f ( σ a ) + ϵ (1) where the function f ( σ a ) is modelled with a PINN with a stress amplitude σ a as input, and ϵ is modelled as an input-varying Gaussian distribution described as ϵ ∼ Gaussian (0 , Ω ) (2) where Ω is the variance. The assumption is that the deviation from the regression model follows a Gaussian distribu tion, where the PINN regression model will be used as mean function in the Gaussian distribution. 2. Methods

2.1. PINN Regression

Machine learning regression can be used to replace classical regression that is typically used for defining a fatigue model based on stress and fatigue lives. Since fatigue models established through classical regression are described in e.g. the ISO standard, this type of model will be referred to as the ”ISO model”. ML models such as neural networks enables continuous models that can take both an upper limit, e.g. yield stress, and a lower limit, e.g. fatigue limit, into account. A neural network can be adopted to describe these complicated functions by design. A neural network