Although machine learning methods have demonstrated
promising potential in fatigue crack propagation prediction, they are currently
limited by insufficient incorporation of physical constraints, low model
interpretability, and suboptimal predictive accuracy. These limitations
restrict the reliability of data-driven models on complex engineering
structures, in which fatigue crack propagation is governed by nonlinear
interactions across multiple length scales and loading conditions. When
explicit physical information is lacking, models may output unstable
predictions and cannot be generalized by extrapolating beyond the training data
domain. To accurately predict
multiscale fatigue crack propagation behavior while enhancing the physical
consistency, interpretability, and generalization capability, the present
authors investigated the multi-scale fatigue crack propagation behavior of 304
austenitic stainless steel samples using
an artificial
neural network (ANN). As purely data-driven models cannot properly
represent complex crack propagation across different scales,
the authors
incorporated physics-informed features into the ANN framework, creating a
feature-extended neural network (FENN) that incorporates prior physical
knowledge related to fatigue crack propagation. Next, a multi-scale fatigue
crack propagation mechanism was coupled into the PENN model, establishing a
physics-informed neural network (PINN) model that can explicitly integrate
physical constraints into the learning process. The ANNs more accurately
predicted multi-scale fatigue crack propagation than the traditional
light-gradient boosting machine, extreme gradient boosting, and ridge
regression machine learning methods. The neural-network-based models well-fitted the nonlinear data of fatigue
crack growth data under multi-scale conditions. Expanded with physics-informed
features, the FENN model improved the prediction accuracy by 7.23% and 18.75%
on the training and testing datasets, respectively, relative to the baseline
ANN, confirming the effectiveness of physical feature embedding. Incorporating
the physical information into the learning framework significantly
enhanced both the training performance and generalization capability. The prediction accuracy was further improved
in the PINN model, which integrates multi-scale physical mechanisms to capture
the complex patterns of fatigue crack propagation across different scales. The
PINN model is robust with good error controllability and high generalization
capability. This performance improvement demonstrates the advantage of
combining data-driven learning with explicit physical constraints into
multiscale fatigue crack propagation prediction. To improve the transparency and physical interpretability of the model,
the decision-making process of the PINN model was interpreted through the
SHapley Additive exPlanations (SHAP) method, which quantitatively evaluates the
contribution of each input feature to the model’s prediction. The
SHAP-based analysis determines the relative importance of different input
variables, further supporting the physical rationality and reliability of the
proposed PINN model.