DeepOFormer: Deep Operator Learning with Domain-informed Features for Fatigue Life Prediction

TL;DR

This work addresses fatigue-life prediction for aluminum alloys under data scarcity by formulating S-N curve prediction as an operator learning task. The proposed DeepOFormer uses a Transformer-based encoder to process material-domain features alongside a trunk network for stress-domain features, combining their embeddings to predict $\log(N)$ via an operator-like dot product, trained with a mean L2 relative error loss $\ell_{ML2RE}$. On a dataset of 54 S-N curves, DeepOFormer with three domain-informed features and ML2RE achieves $R^2=0.9515$, MAE $=0.2080$, and MRE $=0.5077$, outperforming DeepONet, TabTransformer, and XGBoost. The study demonstrates improved accuracy and generalization for fatigue life prediction in aluminum alloys, with future work focusing on dataset expansion and physics-informed constraints to enhance robustness and applicability.

Abstract

Fatigue life characterizes the duration a material can function before failure under specific environmental conditions, and is traditionally assessed using stress-life (S-N) curves. While machine learning and deep learning offer promising results for fatigue life prediction, they face the overfitting challenge because of the small size of fatigue experimental data in specific materials. To address this challenge, we propose, DeepOFormer, by formulating S-N curve prediction as an operator learning problem. DeepOFormer improves the deep operator learning framework with a transformer-based encoder and a mean L2 relative error loss function. We also consider Stussi, Weibull, and Pascual and Meeker (PM) features as domain-informed features. These features are motivated by empirical fatigue models. To evaluate the performance of our DeepOFormer, we compare it with different deep learning models and XGBoost on a dataset with 54 S-N curves of aluminum alloys. With seven different aluminum alloys selected for testing, our DeepOFormer achieves an R2 of 0.9515, a mean absolute error of 0.2080, and a mean relative error of 0.5077, significantly outperforming state-of-the-art deep/machine learning methods including DeepONet, TabTransformer, and XGBoost, etc. The results highlight that our Deep0Former integrating with domain-informed features substantially improves prediction accuracy and generalization capabilities for fatigue life prediction in aluminum alloys.

Figures (4)

• Figure 1: Screenshot of the fatigue dataset used in this paper.
• Figure 2: DeepOFormer architecture for fatigue life prediction. A transformer network (light green) encodes features $u=$ [UTS, TYS, Fatigue Strength, Temper, R], while the trunk network (light blue) processes stress-related and domain-informed features $y=$ [$\sigma_a$, $\sigma_a^3$, Stüssi, Weibull, PM]. The final $\log(N)$ is obtained via the operator-based dot product of the two embeddings.
• Figure 3: Predicted S-N curves (red circles) versus the true S-N curves (blue squares) for six selected S-N curves. The shaded region denotes $\pm 2\sigma$ from ten repetitions, illustrating the model's uncertainty. The $x$-axis shows the number of cycles ($N$) in the logarithm scale, and the $y$-axis is the stress amplitude $\sigma_a$.
• Figure 4: Predicted vs. true $\log(N)$ on the test set, with error bars showing $\pm 2\sigma$ from ten repetitions. The diagonal line indicates perfect prediction.