The experimental data used in this research are obtained from the NIMS Structural Materials Data Sheet Service, a publicly available collection of fatigue data sheets published by the National Institute of Materials Science^[29]. Table 1 presents data on HT and high-cycle fatigue performance for the steel grades under the specified fatigue testing conditions.

Given the wide dispersion of fatigue life values relative to other parameters, the data are transformed using the base-10 logarithm for analysis. After data processing, two datasets representing fatigue performance at RT and HT are formed. The RT dataset consists of 60 data points, while the HT datasets at 400, 500, and 600 °C comprise 50, 59, and 45 data points, respectively. Each data point consists of 29 features, including processing details, chemical composition, mechanical properties, stress amplitude (σ), and target life (logNf). The chemical composition includes C, Si, Mn, P, S, Ni, Cr, Mo, W, etc., the processing details include ingot size (Is), reduction ratio (Rr), non-metallic inclusions (dA, dB, dC), austenite grain size number (Ags) and the mechanical properties include tensile strength (TS), 0.2% proof stress (YS), true fracture stress (TFS), elongation (EL) and reduction of area (RA). The distributions of these variables and the target attribute, fatigue life, are illustrated in Figure 2. A summary of the feature variables, including their full descriptions and abbreviations, is presented in Supplementary Table 1.

Before performing ML, the collected data are pre-processed by normalizing each variable to the [0, 1] interval using the following equation, which eliminates the influence of differing measurement scales on model predictive performance^[30].

(1) $$ x'=\frac{x-\mathrm{min}(x)}{\mathrm{max}(x)-\mathrm{min}(x)} $$

where x is the original data value, x′ is the normalized result, min(x) and max(x) are the minimum and maximum values in the dataset, respectively.

In this study, six regression algorithms, including Ridge, Lasso, random forest (RF), extreme gradient boosting (XGBoost), categorical boosting (CatBoost), and gradient boosting decision tree (GBDT), are used to model fatigue life. The six models are selected to provide a balanced comparison between interpretable linear methods and powerful nonlinear ensemble techniques. Ridge and Lasso are linear regression models with L2 and L1 regularization, respectively, that help prevent overfitting when dealing with high-dimensional features. However, their linear nature limits their ability to capture the complex nonlinear relationships common in fatigue behavior. In contrast, RF and boosting algorithms, including XGBoost, CatBoost, and GBDT, are ensemble methods that can model nonlinear interactions without requiring explicit functional forms. RF reduces overfitting by averaging predictions from multiple decision trees. XGBoost efficiently handles missing values and uses regularization to control model complexity. CatBoost is specifically designed to handle categorical features and reduce overfitting. GBDT provides a flexible framework with robust performance across various datasets. Despite their strengths, ensemble methods are generally more computationally expensive and sensitive to hyperparameter tuning^[31,32].

The efficacy of these models is assessed using four key evaluation metrics, namely the coefficient of determination (R²)^[33], root mean square error (RMSE)^[34], mean absolute error (MAE)^[35], and Pearson correlation coefficient (PCC)^[36]. R² quantifies the proportion of variance explained and serves as the primary metric for assessing a regression model’s goodness of fit, with values closer to 1 indicating greater model accuracy. MAE measures the average magnitude of errors without emphasizing large deviations, offering robustness to outliers, while RMSE calculates the square root of the mean squared error and is more sensitive to large errors. For both metrics, smaller values indicate higher predictive accuracy^[37,38]. In regression problems, the PCC can be used to evaluate a model’s predictive accuracy by quantifying the linear correlation between the predicted and true values. It ranges from -1 to 1, with values close to 1 or -1 indicating a strong linear relationship and values near 0 indicating no linear correlation. These evaluation metrics are defined in Equations (2)-(5).

(2) $$ R^2=1-\frac{\sum_{i=1}^n(y_i-\hat{y}_i)^2}{\sum_{i=1}^n\frac{1}{n}(y_i-\bar{y})^2} $$

(3) $$ RMSE=\sqrt{\sum_{i=1}^n\frac{1}{n}(\hat{y}_i-y_i)^2} $$

(4) $$ MAE=\frac{1}{n}\sum_{i=1}^n|\hat{y}_i-y_i| $$

(5) $$ PCC=\frac{\sum_{i=1}^n(y_i-\bar{y})(\hat{y}_i-\bar{\hat{y}})}{\sqrt{\sum_{i=1}^n(y_i-\bar{y})^2\sum_{i=1}^n(\hat{y}_i-\bar{\hat{y}})^2}} $$

where y_i, $$ \hat{y}_i $$, $$ \bar{y} $$, and $$ \bar{\hat{y}} $$ denote the actual value, predicted value, the mean of actual values, and the mean of predicted values, respectively, with n representing the total number of samples.

To prevent overfitting while maximizing data utility, model evaluation is performed using 10-fold cross-validation^[39]. This method divides the data into 10 subsets, each serving as the validation set in turn, with the remaining subsets forming the training set. This strategy is particularly beneficial for limited data, as it ensures that all data points participate in both training and validation phases, thereby enabling a thorough and reliable assessment of model performance. Each model underwent 50 independent training runs with diverse random seeds to enhance the stability and reliability of the results. The averaged R², RMSE, MAE and PCC values are reported, with the standard deviation across repeated runs used as error bars. The hyperparameters of each model are automatically optimized using Optuna, and the corresponding parameters for all models are listed in Supplementary Table 2.

The RT fatigue life is modeled using six regression algorithms with the full feature set. The evaluation metrics of these models are summarized in the radar chart shown in Figure 3A. The GBDT model demonstrates superior performance compared with the others. The scatter plot of experimental values vs. average predicted values, along with the corresponding residual plot for the GBDT model, both with error bars, is presented in Figure 3B. The GBDT model achieves the highest R² of 0.895 (± 0.022) and PCC of 0.949 (± 0.011), and the lowest RMSE of 0.313 (± 0.030) and MAE of 0.230 (± 0.020). The model’s high accuracy in predicting fatigue life in the RT dataset is evidenced by the close alignment of most data points with the line of best fit. The residual plot shows a relatively random distribution around the zero line, with residuals predominantly confined to ± 0.5 units across the experimental range. A slight heteroscedasticity is evident, with marginally greater dispersion at higher experimental logNf values (> 6.5), indicating increased prediction uncertainty in the upper regime. The approximately symmetric scatter above and below the zero reference line corroborates the absence of significant prediction bias. The performance of the remaining models is shown in Supplementary Figure 1.

Feature selection is a critical step in optimizing ML models, as it reduces complexity and computational cost by identifying and retaining only the features with the highest information content. This process not only improves model performance by mitigating overfitting but also enhances interpretability by clarifying the key factors driving predictions. Using SHapley Additive exPlanations (SHAP)^[40] to rank and visualize feature importance significantly enhances the interpretability of fatigue life models. This method assigns each feature a consistent importance value based on its contribution to predictions, thereby uncovering key interactions between input variables and the target. The significance of these characteristics regarding fatigue life at RT is shown in Figure 4, and the feature importance under HT is shown in Supplementary Figure 2.

In Figure 4A and B, each point represents a SHAP value, and the color encodes the feature value according to the color bar (warmer colors indicate larger feature values, cooler colors indicate smaller feature values). When points with warmer colors cluster on the right (positive SHAP values), larger feature values tend to increase the prediction. The full ranking of feature importance guides the selection of the optimal subset. Feature importance analysis for fatigue life prediction identified σ, TS, YS, W, dB, EL, TFS, RA, Cu, and Mn as the ten most influential features, which are therefore selected for model inclusion. To further refine the feature set, the optimal subset method is applied^[41]. This statistical approach evaluates all possible combinations of features to identify the subset that provides the best fit according to the specified model criteria. This method fits a least-squares model to every possible feature combination, from single features to the full feature set, and selects the best subset based on a comprehensive performance comparison.

The result of the optimal subset selection for the RT dataset is shown in Figure 4C. Due to the large number of feature subsets, only the best subsets for each subset size are shown. The analysis indicates that model performance improves with an increasing number of features, as evidenced by a rise in R² and a corresponding decrease in RMSE. Both metrics stabilize after five features are included, suggesting that additional features contribute little to further improvement. An optimal feature subset consisting of five variables (W, YS, TFS, EL, and σ) is identified to balance predictive accuracy and model complexity. Through an exhaustive search, this subset is the optimal five‑feature combination in terms of R² for the current dataset, and its robustness is confirmed by 10‑fold cross‑validation with 50 diverse random seeds. From a physical perspective, σ directly governs the applied stress level and is inversely correlated with fatigue life. YS and TFS reflect the material’s resistance to plastic deformation and fracture, respectively, both of which are critical under cyclic loading. EL represents ductility, which influences fatigue crack initiation and propagation. The W content can improve fatigue performance through solid solution strengthening and precipitation hardening induced by fine particles, thereby enhancing the alloy’s fatigue resistance^[42]. The inclusion of these five features thus captures the key factors governing fatigue behavior while maintaining model simplicity.

The five features identified through feature selection in the previous section are used as inputs to the ML model. The performance of the diverse models is shown in the radar chart in Figure 5A. Compared with the case using all features, no significant degradation in model performance is observed, indicating the reasonableness of the feature engineering process. Among the six evaluated ML models, the GBDT model again demonstrated the highest prediction accuracy, achieving the highest R² (0.893 ± 0.023) and PCC (0.948 ± 0.012), along with the lowest RMSE (0.317 ± 0.032) and MAE (0.234 ± 0.020). The scatter plot of the GBDT model showing the relationship between the experimental and predicted values, along with the corresponding residual plot, is shown in Figure 5B. The predictions are in close agreement with the experimental values, with relatively small errors. Therefore, the GBDT models developed in this study demonstrate satisfactory predictive capability and stability for fatigue life prediction within the compositional scope of the original dataset, as evidenced by R² values exceeding 0.85 and error bars smaller than 0.03. The residuals show an approximately symmetric distribution around the zero baseline, with most data points clustered within a narrow ± 0.5 interval. A slight deviation is observed at the lower and upper ends of the dataset. The residual variance is smaller for the experimental logNf values below 4.5, whereas a larger spread with a few positive residuals is observed for the values above 7.0, indicating reduced prediction accuracy in these regions. In the central range of experimental logNf (5.5-6.8), the residuals are randomly distributed around zero with small bias. Additionally, the detailed performance of the remaining models on the RT dataset after feature selection is presented in Supplementary Figure 3.

Directly applying the GBDT model trained on RT data to predict HT fatigue life yields poor results and shows virtually no predictive capability. This discrepancy underscores the model’s inadequacy in predicting HT behavior when trained solely on RT data. Physically, HT exposure induces substantial microstructural evolution in steels, including recovery, recrystallization, precipitate coarsening, and dislocation structure rearrangement. Consequently, fatigue resistance and failure mechanisms differ fundamentally between RT and HT conditions. Even when the chemical composition and loading conditions remain identical, the underlying physical processes governing fatigue life are not directly transferable. Statistically, the relationship between input features and fatigue life shows a domain shift from RT to HT, indicating that the feature-target distributions in the two domains are misaligned. To bridge this domain gap, the TL strategy detailed in Section “MATERIALS AND METHODS” is employed. In this strategy, RT fatigue life serves as the source domain, while HT fatigue life constitutes the target domain. To implement TL effectively, feature selection is first performed on the HT data to align feature importance with that of the RT dataset. Using the optimal subset method, the key features for HT fatigue life are identified. As illustrated in Figure 4D, the optimal feature set comprising W, YS, TFS, EL, and σ aligns closely with the feature set derived from RT data. Furthermore, feature selection was performed at elevated temperatures of 500 and 600 °C, and the results exhibited the same characteristics as those observed in the RT dataset, as shown in Supplementary Figure 4. Building on these selected features, TL is applied by training a model on RT fatigue data to predict HT fatigue life, thereby mitigating the challenge of limited HT data availability. By incrementally increasing the proportion of HT data during training, the model is continuously refined to better capture material behavior under elevated temperatures, which reduces prediction discrepancies and improves generalization across varying thermal conditions.

The performance of the GBDT model is systematically evaluated by progressively incorporating HT data into the RT training set in 10% increments, from 10% to 90%. The remaining HT data are reserved as a test set. Additionally, the efficacy of the TL strategy is verified using a dataset containing only HT data for comparison. To ensure robustness, each configuration is trained 50 times using different random seeds. As illustrated in Figure 6A, the average R² values from both evaluation strategies increase monotonically as HT data are incorporated, indicating that the model progressively adapts to the target domain. For the HT-only model, the R² values are 0.368 and 0.825 when 30% and 60% HT data are used, respectively. More importantly, across all HT data fractions, the model trained on the combined RT-HT dataset consistently outperforms the model trained solely on HT data, demonstrating that knowledge learned from the data-rich RT domain provides a beneficial initialization and significantly enhances predictive capability under limited HT data conditions. This result highlights the necessity of the TL strategy, particularly when HT data are scarce. The GBDT model achieves the best performance on the RT dataset and is therefore initially considered suitable for TL from RT to HT. However, this remains an assumption, so TL from RT to HT is performed for all models as shown in Supplementary Figures 5-9, and the GBDT model is ultimately selected after a comprehensive comparison of their performance.

The averaged performance over 50 iterations for mixing ratios of 0%, 30%, and 60% HT data is shown in Figure 6B-D, respectively. When no HT data are included [Figure 6B], the model exhibits poor predictive capability, with negative R² values, indicating a difference between the RT and HT domains. Incorporating 30% HT data yields moderate predictive accuracy (R² = 0.651), while increasing the fraction to 60% significantly improves performance (R² = 0.912), accompanied by substantial reductions in RMSE and MAE and a marked increase in PCC. This improvement is further corroborated by the evolution of the residual distributions. As shown in Figure 6B-D, the residuals progressively transition from systematic bias to stochastic dispersion as HT data increase. At 0% HT data, residuals show pronounced negative deviations across the entire prediction range, indicating a systematic overestimation of fatigue life. With 30% HT data, the residual distribution becomes approximately symmetric around zero, although noticeable variance and heteroscedasticity persist, particularly at higher fatigue life levels. When the HT fraction reaches 60%, residuals collapse into a narrow and homoscedastic band, indicating stable and unbiased predictions. The progressive performance improvement with increasing HT data reflects the model’s enhanced adaptation to the target domain through the incorporation of HT information. Transfer predictions are further investigated across temperatures ranging from RT to 500 °C and from RT to 600 °C, as presented in Supplementary Figures 10 and 11, respectively. These results not only confirm the effectiveness of the TL strategy but also provide empirical evidence for consistent fatigue behavior patterns across temperatures, thereby fundamentally justifying the applicability of TL in this context.

The present strategy is fundamentally data-driven and does not explicitly incorporate microstructural evolution or temperature-dependent deformation mechanisms. Although consistent feature subsets are identified across RT and HT datasets, this consistency reflects similarity in predictive relevance rather than mechanistic equivalence. The failure of direct RT-to-HT prediction indicates a significant domain gap, whereas improved performance with increasing HT data suggests that model adaptation relies on partial retraining. Therefore, the proposed approach should be understood as a TL strategy that improves data efficiency rather than a strict transfer of physical knowledge. HT fatigue involves additional mechanisms such as creep-fatigue interaction, oxidation-assisted damage, and microstructural instability, which are not explicitly captured in the present strategy due to data limitations^[43]. Instead, their effects are indirectly embedded in macroscopic descriptors such as strength and elongation.

The input features include compositional, processing, and macroscopic mechanical descriptors, which are used to establish predictive relationships with fatigue life. These descriptors are treated as static, global variables and do not explicitly capture microstructural evolution or local damage processes during fatigue. Although microstructural features such as grain size and inclusion characteristics are included, their roles are represented only through statistical correlations rather than explicit mechanistic modeling. Consequently, SHAP-based feature importance reflects predictive relevance rather than causal relationships between microstructure, deformation, and fatigue damage evolution. The observed feature consistency across temperatures therefore indicates similarity in statistical patterns within the dataset, rather than invariance of the underlying physical mechanisms. Given the current data availability, macroscopic properties such as strength and elongation can be regarded as integrated surrogate descriptors that implicitly capture the combined influence of microstructure and its evolution. However, incorporating microstructure-sensitive descriptors and explicitly modeling temperature-dependent microstructure evolution remain necessary to improve physical interpretability and extrapolation capability in future work. Importantly, the proposed TL strategy is developed and validated specifically for alloy steels under the testing conditions summarized in Table 1 (rotating bending, load control with zero mean stress, 125 Hz).