Researchers have developed a neural network that pairs a physics-based module built on Basquin's formula with a purely data-driven component to estimate how long materials survive repeated loading, according to a study published in Nature on 21 October 2026. The work, carried out at the Rocket Force University of Engineering in Xi'an, China, describes a model the authors call a prior knowledge-informed neural network (PKiNN). Experimental tests indicated the approach extrapolates better than conventional machine learning methods, Nature reports.
Why it matters
Fatigue life — the number of cycles a part can endure before it fails under cyclic stress — is a central concern in engineering, from aircraft components to rocket propulsion hardware. Getting that estimate right matters for safety and for design margins. The study's authors say their hybrid model offers an advantage over standard machine learning in situations where predictions must extend beyond the conditions seen during training, a common weakness of purely data-driven approaches.
How the two modules work together
The PKiNN architecture splits the prediction task into two parts. One module encodes prior knowledge, generating data that follows the characteristics of an S-N curve, the standard plot relating applied stress to the number of cycles a material withstands before failure. The second module operates without that physics input, learning from data to account for effects such as stress concentration caused by notches.
The outputs of both modules are then combined through a single-layer fully connected neural network, which produces the final fatigue life prediction. In effect, the model uses established fatigue theory as a foundation while letting the data-driven side handle geometric and other influences that the formula alone does not capture.
What the experiments showed
According to Nature, experimental validation confirmed that PKiNN outperformed traditional machine learning approaches in extrapolation — the ability to make sound predictions outside the range of its training data. The study also reports that the model's predictive performance depends less on which specific training dataset is chosen, a contrast with current informed machine learning methods that can be sensitive to that selection.
The research was supported by the Natural Science Basic Research Program of Shaanxi under two grants, and by the Stable Support Project of the National Key Laboratory of Solid Rocket Propulsion. The authors are affiliated with the National Key Laboratory of Solid Rocket Propulsion and the College of Launch and Power Engineering, both at the Rocket Force University of Engineering in Xi'an.
The paper is published open access in Scientific Reports under a Creative Commons licence that permits non-commercial sharing with attribution. The citation lists Yang, D., Wang, Y., Guo, J. and colleagues as authors.
What to watch: whether independent groups test the PKiNN approach on materials and loading conditions beyond those in the study, which would show how far its extrapolation advantage holds.
