Integrating physical metallurgy principles and machine learning for predicting continuous cooling phase transformations in steel

Data collection and feature engineering

This study systematically reviewed published literature on steel CCT diagrams from the past two decades, covering a wide range of steel grades. To ensure data reliability, the initial screening prioritized sources providing comprehensive experimental parameters, including chemical composition, austenitizing temperature and time, deformation conditions, and metallographic verification of microstructure. Key phase transformation points were then extracted from the reported CCT curves using the image digitization tool in Origin software.

The data extraction process is as follows: temperature units were standardized to Celsius, time units to seconds, and the time axis was converted to a logarithmic scale, log(t). Original curve images were imported into the software, where horizontal and vertical coordinate ranges were manually defined, and the coordinate system was mapped using the origin and the points of maximum temperature and time. The start and finish temperatures of each phase transformation, along with their corresponding times (t), were then systematically extracted point-by-point from the CCT curves using the sampling method shown in Figure 1. Data points that were ambiguous in phase-transformation inflection identification or showed abrupt temperature jumps inconsistent with the local digitization/readout from the same source (i.e., apparent digitization or tracing artifacts) were excluded standard data-validation practice for curated experimental/digitized materials data. Genuine, physically meaningful non-monotonic behavior was retained. The screened dataset preserves the original experimental variability while removing only clear extraction errors to avoid spurious interference in subsequent ML models. The digitization process inevitably introduces reading errors associated with image resolution and coordinate mapping. Based on repeated extractions of selected CCT curves, the estimated uncertainty in transformation temperatures is within ±3-5 °C, which is comparable to the typical experimental scatter of dilatometric measurements and is therefore not expected to affect the model conclusions.

Figure 1. Data points extracted from the CCT diagrams using an image digitization tool. CCT: Continuous cooling transformation; F_s: ferrite transformation start temperature; F_f: ferrite transformation finish temperature; P_s: pearlite transformation start temperature; P_f: pearlite transformation finish temperature; B_s: bainite transformation start temperature; B_f: bainite transformation finish temperature; M_s: martensite transformation start temperature; M_f: martensite transformation finish temperature; T_A: austenitizing temperature; t_A: austenitizing time; CR: cooling rate.

Finally, all data were consolidated into an Excel spreadsheet to establish a comprehensive database. The database fields include 16 chemical elements (C, Si, Mn, Ni, Cr, Mo, V, Al, Ti, Nb, B, P, S, Cu, W, N); 8 phase transformation temperatures (F_s, F_f; P_s, P_f; B_s, B_f; M_s, M_f); 3 continuous cooling parameters (austenitizing temperature T_A, austenitizing time t_A, cooling rate CR); and 3 deformation process parameters (deformation amount ε, deformation temperature T_ε, deformation rate $$ \dot{\varepsilon} $$). Among them, the 8 phase transformation temperatures serve as target outputs for ML regression. All other parameters were stored as raw candidate features. After feature selection and PM-based feature engineering, partial raw parameters were discarded, and the final input features were determined.

To account for the effect of deformation on phase transformation kinetics, two key supplementary input features were calculated based on PM principles: dislocation energy ΔG_D and austenite grain size D_γ.

Calculation of ΔG_D begins by determining the flow stress (σ) through the Arrhenius model [Equation (1)], which links deformation parameters with material properties. The material constants A, β, and n are obtained using the model by Hatta et al.^[32], and the carbon content of the material, while the deformation activation energy Q is evaluated according to the model developed by Medina et al. and the chemical composition^[33]. Once the flow stress σ is obtained, it is substituted into Equation (2) to calculate ΔG_D.

where the Taylor factor M is 3.11 [for face-centered cubic (FCC) metals], the shear modulus G is 79 GPa (representing austenitic shear modulus), and the constant α is 0.15 (for FCC metals)^[8,34]. It should be noted that Equation (2) directly yields the dislocation stored energy per unit volume with dimensions of J/m³. In this work, we report the ΔG_D values in kJ/m³ to keep the numerical range convenient for subsequent ML processing.

For D_γ, the austenite grain size, the model proposed by Wang et al. is adopted^[35]. This model calculates grain size from material composition and austenitizing parameters, as given in^[35]:

where the chemical composition (in wt.%), austenitizing temperature T_A, and austenitizing time t_A are sourced from the database, and R is the universal gas constant, typically taken as 8.314 J/(mol·K). Notably, the obtained D_γ represents the prior-austenite grain size before hot deformation; grain-refinement effects induced by deformation are not incorporated here and are instead characterized by ΔG_D. The successful construction of two supplementary PM input features enhances the interpretability and rationality of the ML model.

A total of 64 sets of steel CCT curve data were collected, yielding nearly 13,000 data points for phase transformation start temperatures and almost 11,000 data points for finish temperatures. Model inputs include 16 elemental compositions, austenitizing temperature T_A, cooling rate CR, deformation amount ε, as well as two computationally derived PM parameters ΔG_D and D_γ. The raw parameters t_A, T_ε, and $$ \dot{\varepsilon} $$ are required to calculate ΔG_D and D_γ, and their physical effects on phase transformation are encoded within these two derived features; hence they are not directly fed into the ML models. The eight phase transformation temperatures are the target variables to be predicted. Table 2 presents descriptive statistics for all variables in the database, illustrating the range and variability of the data. To visualize data distribution, this section presents histograms of each input feature. Supplementary Figure 1A and B shows the distribution histograms for phase transformation start and finish temperatures, respectively.

As shown in Table 2 and Supplementary Figure 1, the database covers a carbon content range of 0.09-0.84 wt.%, capturing both low-carbon and high-carbon steels. Alloying elements such as Si, Mn, and Cr exhibit a broad distribution, and the cooling rate range spans from 0.003 to over 600 °C/s, demonstrating strong data representativeness. The database is primarily composed of low-alloy steel data, providing relatively comprehensive material information, although data on high-alloy compositions are relatively sparse.

Although this sparsity may affect the accuracy of predictions for certain alloys, it increases the scalability and generalization of the model across a wider compositional space. In contrast to most existing CCT prediction ML models, which typically focus on static heat-treatment conditions and are limited to low-alloy steels or specific grades^[36], this database extends coverage to high-carbon and complex high-alloy systems, improving model universality. Furthermore, by incorporating actual hot-deformation parameters, such as deformation amount and deformation temperature, the database supports the development of a dynamic phase transformation prediction model tailored to the hot-rolling process.

Additional descriptions of dataset visualization, featurescreening procedures, hyperparameter optimization, and model performance metrics are provided in Supplementary Materials.

Data preprocessing and feature selection

High-quality data forms the basis for building accurate and reliable ML models. Systematic preprocessing and feature selection of raw data prior to model training can effectively improve predictive performance and generalization. In this study, Python toolkits such as NumPy, Pandas, and Matplotlib were used for data preprocessing, including data cleaning, handling missing values, outlier removal, data standardization, and feature correlation analysis. These steps establish a robust foundation for developing a high-precision steel CCT curve prediction model.

The constructed steel CCT curve database contains multidimensional features, several of which include missing values, outliers, and duplicate samples that must be addressed before modeling. Missing values not critical to phase transformation were interpolated, while others, along with anomalous and duplicate samples, were removed. To standardize inputs for K-NN modeling, Z-score normalization was applied, ensuring a mean of 0 and a standard deviation of 1, as given in:

where x is the raw data, μ is the mean, σ is the standard deviation, and Z is the standardized data.

To reduce model complexity and improve computational efficiency, input features were filtered prior to modeling. The Pearson correlation coefficient was used to assess the linear relationship between each feature and the target phase transformation temperature, as given in:

where x_i and y_i are the feature values, and $$ \bar{x} $$ and $$ \bar{y} $$ are the corresponding mean values. Correlation coefficients between each feature and the target variable were calculated using Pandas. Features with absolute correlation coefficients below 0.1 were removed, and these discarded features are listed in Supplementary Table 1. This process eliminates redundant information, enhancing both model training efficiency and interpretability.

ML modeling

RF and K-NN are selected in this work. On one hand, the ensemble-based RF features favorable modeling stability and enables interpretable feature quantification via SHAP analysis, which well accommodates the nonlinear phase transformation behavior coupled with PM parameters. On the other hand, K-NN follows a straightforward principle without explicit function fitting. The two algorithms with distinct modeling mechanisms can be cross-compared to objectively verify the reliability of the established database and input feature system. Using the optimized database, RF and K-NN regression models were constructed, with the data split into training and testing sets in a 7:3 ratio^[37], to assess model interpolation performance within the collected dataset. Hyperparameter optimization was performed using an exhaustive grid search combined with five-fold cross-validation on the training set. For the RF model, key parameters such as the number of decision trees (n_estimators; searched over [10, 20, ..., 200]) and maximum depth (max_depth; searched over [1, 10, 20, 30, 50]) were primarily optimized, while for the K-NN model, the number of neighbors (n_neighbors; searched over [1, 2, ..., 8]) and the weight calculation method (weights; searched over [uniform, distance]) were refined. The optimal configuration was identified as n_neighbors = 2 with distance weighting. To eliminate scale effects in distance calculation, Zscore standardization (zero mean and unit variance) was applied to the KNN training data, performed within each training fold to prevent data leakage. The main objective was to minimize root mean square error (RMSE) on validation folds, while monitoring mean absolute error (MAE) and coefficient of determination (R²) for comprehensive performance assessment. The final optimal parameters for both models are presented in Supplementary Tables 2 and 3, respectively.

It should be noted that approximately 24,000 data points were extracted from 64 CCT curves (each corresponding to a unique steel grade and source publication). Points from the same CCT curve, steel grade, or literature source are therefore not statistically independent. In the present study, the dataset was randomly divided into training and test subsets in a 7:3 ratio mainly to evaluate the prediction accuracy under the original research objective - i.e., fitting and prediction within the scope of the collected literature data and known steel grades/processing conditions. This random partitioning facilitates the assessment of model performance on interpolation among already-seen materials, but it does not guarantee independence between the training and test sets in terms of CCT curve, steel grade, or literature source.

Model validation based on thermal expansion tests

To rigorously validate the model ability to generalize to new data, a comprehensive study was performed using 30CrMnSi steel produced by a specific steel mill (detailed chemical composition provided in Table 3). Both static (without deformation) and dynamic (with deformation) thermal expansion experiments were systematically designed to cover a range of thermal and mechanical conditions.

For the static experiments, a Formastor-F II phase transformation analyzer was utilized. Cylindrical samples were first austenitized at 1,000 °C for 60 s to ensure a uniform austenite microstructure. Subsequently, the samples were cooled to 900 °C and held for 60 s to stabilize the austenite phase. The final cooling was performed at controlled rates varying from 0.1 to 100 °C/s, allowing for detailed observation of phase transformations across different thermal gradients. Dynamic experiments were conducted using a DIL 805A/D simulator. After austenitization at 1,000 °C for 60 s, samples were rapidly transferred to the deformation stage at 900 °C. At this stage, a true strain of 0.4 was applied at a controlled strain rate of 0.1 s^-1, simulating industrial thermo-mechanical processing conditions, followed by cooling at a rate of 0.1-100 °C/s, enabling direct comparison between the two experimental modalities.

The experimental procedures for both static and dynamic tests are illustrated in the flowcharts in Figure 2. Figure 3 presents representative dilatation curves at different cooling rates. Critical phase transformation points at each cooling rate were quantitatively determined using the tangent method^[38], and the corresponding results are systematically summarized in Tables 4 and 5. To directly correlate the thermal processing history with the resulting microstructure, metallographic analyses were carried out on specimens cooled to room temperature at various rates. Figure 4A and B provides optical micrographs for the static and dynamic experimental conditions, respectively, visually demonstrating the evolution of microstructural features as a function of cooling rate and processing mode. It should be noted that for the cooling rate of 1 °C/s, trace grain‑boundary pro-eutectoid ferrite can be identified by metallographic observation. Nevertheless, the volume fraction of ferrite is quite low; its dilatometric signal is overlaid by the subsequent strong bainite‑transformation response, so reliable F_s and F_f values cannot be extracted via the tangent method.

Figure 2. Flowchart of CCT experiments. (A) Static experiment; (B) Dynamic experiment. CCT: Continuous cooling transformation.

Figure 3. Dilatation curves of 30CrMnSi steel at different cooling rates. (A) Static experiment; (B) Dynamic experiment. Different colors and line styles represent different cooling rates as indicated in the legend.

Figure 4. Microstructure of 30CrMnSi steel at different cooling rates. (A) Static specimen; (B) Dynamic specimen. F: Ferrite; P: pearlite; B: bainite; M: martensite.

Evaluation of ML model performance

The prediction performance of each ML model on the heldout test subset was comprehensively evaluated using three widely accepted statistical metrics: the R², MAE, and RMSE. The R² value quantifies how well the predicted values explain the observed variance, with a value closer to 1 indicating stronger explanatory power. MAE measures the average magnitude of the errors between predicted and actual values, providing an intuitive sense of prediction accuracy. RMSE penalizes larger errors more strongly. By employing these complementary metrics, the evaluation accounts for both the overall fit and the magnitude of prediction errors, thus providing a robust and logical assessment of model performance.

For the RF model, Figure 5 compares the predicted vs. measured values for the 8 phase transformation temperatures. All data points indicate that the model has extremely high predictive accuracy. As shown by the quantitative metrics in Supplementary Table 4, except for the P_s model (R² = 0.977, MAE = 3.5 °C), the remaining seven transformation targets achieve R² values at or above 0.99, with MAEs controlled around 3.0 °C. Among them, the M_s model provides the most accurate predictions (R² = 0.996, MAE = 1.9 °C), which is related to the mechanism of martensitic transformation being dominated by alloying elements and easily captured by ML models.

Figure 5. Comparison of RF model predictions with measured values. (A) Phase transformation start temperature; (B) Phase transformation finish temperature. RF: Random forest; F_s: ferrite transformation start temperature; P_s: pearlite transformation start temperature; B_s: bainite transformation start temperature; M_s: martensite transformation start temperature; F_f: ferrite transformation finish temperature; P_f: pearlite transformation finish temperature; B_f: bainite transformation finish temperature; M_f: martensite transformation finish temperature.

For the K-NN model, the scatter plot in Figure 6 shows that most predicted values for the target variables align closely with the actual values. This visual pattern suggests that the K-NN model generally captures the underlying relationships in the data. However, a closer examination of the quantitative results in Supplementary Table 5 reveals that the accuracy for P_f is affected by a relatively high RMSE of 14.5 °C. This elevated error may be attributed to the sensitivity of the K-NN algorithm to local outliers, where predictions can be significantly influenced by nearby anomalous data points. Despite this limitation, the model achieves a reasonable MAE of 3.5 °C for P_f, indicating that its typical prediction errors remain within an acceptable range. In addition, the K-NN model outperforms the RF model in predicting P_s, achieving a higher R² value of 0.980. This superior R² demonstrates that K-NN is particularly effective at capturing local patterns and features in the dataset.

Figure 6. Comparison of K-NN model predictions with measured values. (A) Phase transformation start temperature; (B) Phase transformation finish temperature. K-NN: K-nearest neighbor; F_s: ferrite transformation start temperature; P_s: pearlite transformation start temperature; B_s: bainite transformation start temperature; M_s: martensite transformation start temperature; F_f: ferrite transformation finish temperature; P_f: pearlite transformation finish temperature; B_f: bainite transformation finish temperature; M_f: martensite transformation finish temperature.

A comprehensive evaluation was conducted to compare the performance of the two models across multiple aspects. The bar and line charts in Figure 7A-C visually compare important evaluation metrics for each model. This approach provides clear insight into where each model excels or struggles, highlighting differences in prediction quality for various targets. In addition, 10-fold cross-validation was performed separately for each phase transformation temperature, and the mean R² values from cross-validation are summarized in Figure 7C. The RF model consistently achieved mean R² [cross-validation (CV)] values above 0.980 for all target temperatures, indicating high predictive accuracy and robust performance. In contrast, the mean R² (CV) values for the K-NN model fluctuated significantly and were generally lower than those of the RF model, demonstrating less consistent performance and greater sensitivity to specific data partitions. This inconsistency means that although K-NN can achieve high accuracy for some individual phase transformation temperatures, it does not deliver stable results across all targets. Overall, the RF model demonstrates superior stability in predicting the eight phase transformation temperatures.

Figure 7. Comparison of evaluation metrics between the RF and K-NN models. (A) MAE & RMSE; (B) R²; (C) R² from 10-fold cross-validation. RF: Random forest; K-NN: k-nearest neighbor; MAE: mean absolute error; RMSE: root mean square error; R²: coefficient of determination; CV: cross-validation; F_s: ferrite transformation start temperature; P_s: pearlite transformation start temperature; B_s: bainite transformation start temperature; M_s: martensite transformation start temperature; F_f: ferrite transformation finish temperature; P_f: pearlite transformation finish temperature; B_f: bainite transformation finish temperature; M_f: martensite transformation finish temperature.

To further examine the independence of the test set, we conducted exploratory validation using stricter grouping protocols: GroupKFold with each complete CCT curve treated as one group, leave-one-steel-grade-out validation, and leave-one-source-publication-out validation. These stricter partitioning tests show degraded prediction performance, which qualitatively indicates limited extrapolation ability to unseen steel grades. Given the limited diversity of the current database, the quantitative results from these strict-group validations are not sufficiently robust for formal quantitative analysis in this work. Therefore, the high R² and low MAE values reported above should be interpreted as model performance under the original 7:3 random partitioning, focusing on predictions within the collected conditions, rather than evidence of reliable generalization to entirely new steel grades. Expanding the CCT database and carrying out comprehensive quantitative strict-group validation will be pursued as future work.

Global feature importance analysis

Unlike traditional PM models, ML models present interpretability challenges because internal prediction processes cannot be directly described by established mathematical or physical laws. To overcome this limitation and clarify the process by which ML models make predictions and how input features contribute, this study adopted the SHAP method. This method yields quantitative measures of global feature importance for all input variables. Figure 8A-H provides a comprehensive visualization of the average impact of each feature on predictions for the start and finish temperatures of eight distinct phase transformation temperatures, as well as the influence direction of each feature. This interpretability analysis allows for a deeper understanding of model operation and the physical meaning of important input variables. To facilitate detailed inspection of each transformation temperature, individual high-resolution SHAP summary plots are provided in Supplementary Figures 2-9.

Figure 8. Analysis of the influence of input features on phase transformation temperatures and feature importance based on SHAP. (A) F_s; (B) P_s; (C) B_s; (D) M_s; (E) F_f; (F) P_f; (G) B_f; (H) M_f. SHAP: SHapley Additive exPlanations. ΔG_D: dislocation energy; D_γ: austenite grain size; T_A: austenitizing temperature.

Analysis identifies CR as the most influential variable for predicting phase transformation temperatures, including F_s, P_s, B_s, F_f, P_f, and M_f. For M_s, carbon content becomes the primary determining factor. A negative SHAP value for carbon content indicates that higher carbon content produces a lower M_s, which is consistent with established PM principles reported in the literature^[19,20,39]. Additional elements, such as Cr, Ni, and Si, also exert effects on specific phase transformation temperatures that agree with previously published findings. These consistent observations further support the reliability and scientific validity of the model interpretability framework.

A key result involves the significant contribution of the two supplementary features, ΔG_D and D_γ, which originate from PM model calculations and are incorporated into the input dataset. For example, ΔG_D ranks third in importance for the P_s model and fifth for both the B_f and M_f models, while D_γ achieves third place in B_s and F_f models and fourth in the F_s and P_f models based on SHAP analysis. This evidence strongly supports the value of integrating physically informed features into a ML framework. Incorporating variables that represent metallurgical deformation mechanisms enables the hybrid approach to capture essential influences on phase transformation behavior, effectively bridging the gap between data-driven modeling and physically based understanding.

To further quantify the contribution of the PM-derived features, we compared model performance with and without ΔG_D and D_γ as inputs. As shown in Supplementary Figures 10 and 11, adding these two features consistently improves R² and reduces MAE for most transformation temperatures across both RF and K-NN models. This confirms that the PM-guided feature engineering enhances predictive accuracy beyond the baseline composition and thermal parameters.

Analysis of how deformation affects phase transformation temperatures

To further investigate deformation effects, the dependence plot generated by SHAP analysis revealed how the supplementary input feature, dislocation energy ΔG_D, influences the phase transformation temperature [Figure 9A-H]. When ΔG_D increases, SHAP values for F_s, P_s, B_s, F_f, and M_f also increase, which is qualitatively consistent with the underlying physical mechanism: deformation accelerates phase transformation kinetics. For diffusion-type phase transformations such as ferrite and pearlite, high-density dislocations and subgrains introduced via deformation supply additional nucleation sites. A greater amount of deformation storage energy strengthens the driving force for the phase transformation, increases the diffusion efficiency of elements, and results in higher transformation temperatures. bainite phase transformation mechanism shows considerable complexity; multiple authors report inconsistent results due to varying deformation and transformation conditions^[40]. Nevertheless, a broad consensus exists that deformation of austenite leads to a faster bainite transformation rate, a higher initial transformation temperature, and a wider bainite transformation region in the CCT diagram^[41-43]. These findings align with model output, which shows an increase in B_s as ΔG_D rises. For M_s, deformation exerts minimal influence, reflecting the model ability to recognize that non-diffusive phase transformations respond more to chemical composition than to strain.

Figure 9. SHAP analysis of the effect of ΔG_D on phase transformation temperature prediction. (A) F_s; (B) P_s; (C) B_s; (D) M_s; (E) F_f; (F) P_f; (G) B_f; (H) M_f. SHAP: SHapley Additive exPlanations; ΔG_D: dislocation energy; F_s: ferrite transformation start temperature; P_s: pearlite transformation start temperature; B_s: bainite transformation start temperature; M_s: martensite transformation start temperature; F_f: ferrite transformation finish temperature; P_f: pearlite transformation finish temperature; B_f: bainite transformation finish temperature; M_f: martensite transformation finish temperature.

Validation results based on thermal expansion tests

Experimentally measured static and dynamic CCT curves for 30CrMnSi steel served as benchmarks for evaluating prediction accuracy of both RF and K-NN models, as displayed in Figure 10A and B. These figures also present a direct comparison with results obtained using JMatPro commercial software, providing a comprehensive view of predictive capabilities across all approaches.

Figure 10. Comparison of experimental CCT curves with model-predicted CCT curves. (A) Static CCT; (B) Dynamic CCT. CCT: Continuous cooling transformation; Exp.: experimental value; RF pred.: random forest predicted value; K-NN pred.: k-nearest neighbor predicted value.

Examination of the static CCT curve in Figure 10A demonstrates that both ML models produced reliable and accurate results. For F_s and B_s, predicted values showed close alignment with experimental measurements, and error magnitude decreased as CR increased. MAE for these transformations remained below 25.0 °C, indicating robust model performance. The K-NN model achieves an MAE of 15.0 °C for P_s, while the RF model gives 54.5 °C, representing a reduction of about 39.5 °C with K-NN. This substantial difference may result from overfitting in the RF approach. In contrast, the RF model gave better predictions for M_s, with an average absolute error of 34.0 °C, a 13.0 °C improvement over the K-NN model. This performance likely arises from the ensemble learning framework within the RF model, which enables effective management of complex interactions among alloying elements, an important requirement for accurate M_s prediction. The K-NN model, which relies on distance-based calculations, cannot fully capture such multidimensional relationships. For P_f at low cooling rates, both models showed notable prediction deviations, likely due to a small number of relevant training samples and variability in experimental datasets. For M_f, both models maintained strong agreement with experimental values. In comparison, JMatPro commercial software produced much larger errors for ferrite and pearlite transformation temperatures (~100.0 °C), as well as substantial inaccuracies for B_s and M_s. JMatPro also failed to identify critical cooling rates for phase transformations.

Evaluation of dynamic CCT curves in Figure 10B reveals even stronger advantages for the ML approach. The K-NN model provided accurate predictions for increased transformation temperatures of ferrite and pearlite after deformation, achieving an average absolute error of 10.0 °C for ferrite. For pearlite, prediction accuracy decreased slightly as CR increased. The RF model demonstrated slightly lower accuracy than the K-NN for these two diffusion-controlled transformations. For B_s and M_s, the RF model delivered outstanding results, with average absolute error consistently at 5.0 °C or less, while K-NN produced less accurate predictions for these transformations. For transformation finish temperatures (F_f, P_f, and M_f), both models gave reliable results. Notably, both models captured major physical phenomena associated with deformation, including increased start temperatures for phase transformations, leftward shifting of CCT curves (corresponding to shorter transformation times at a given temperature, i.e., accelerated transformation kinetics), and expansion of transformation regions for ferrite and pearlite. The ML model developed for this study, enhanced with supplementary features based on PM, effectively learned and reproduced the complex effects of thermal deformation on phase transformation behavior. This methodological approach resulted in predictive performance far superior to conventional commercial software.

Incorporating a PM parameter in this study enabled the model to replicate several essential features observed in dynamic CCT curves, including an increased onset temperature and a leftward shift of diffusion-type phase transformations. These phenomena result from enhanced energy storage due to deformation, a factor widely considered crucial in phase transformation kinetics. Although the model captured these core effects, closer examination uncovers limitations that require further discussion. Validation performed by Hedström et al. showed that the largest deviations in B_s prediction occurred for specimens subjected to deformation before cooling^[44]. That analysis highlighted a persistent challenge in modeling, i.e., difficulty in representing the full complexity of thermal deformation history. Most models, including the approach used here, apply simplified PM parameters that aggregate deformation effects into a single or limited set of variables. Such a method cannot fully represent the broad spectrum of microstructural changes caused by real thermal deformation. For instance, changes in grain boundary character, spatial distribution of dislocations, and formation of sub-grains or deformation twins, all phenomena that influence phase transformation behavior, are not captured by a single PM parameter.

Consequently, while trends for F_s, P_s, B_s, and related transformations are reasonably well predicted, notable deviations remain under dynamic conditions, especially for transformation finish temperatures such as B_f. This finding indicates that future models should incorporate more granular microstructural descriptors, potentially using data from advanced characterization techniques or multiscale simulations. Techniques including electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), or three-dimensional atom probe tomography (APT) can provide information on grain orientation, dislocation density, and solute segregation, leading to a more physically accurate representation. Enhanced models would then be better suited to address the subtleties of medium-temperature transformations such as bainite, where multiple mechanisms, diffusional and displacive, interact in complex ways.

The RF model, despite improved performance over other approaches, produced an average absolute error of 34 °C when predicting static M_s. This level of error, although lower than some values reported in the literature, still poses concerns for practical applications. Hedström et al. documented errors in M_s prediction exceeding 130 °C for certain high-carbon, high-chromium steels, attributing much of this discrepancy to reliance on nominal composition as model input^[44]. Using nominal composition overlooks the actual chemical state of austenite, especially in cases where carbide precipitation or incomplete dissolution changes the distribution of carbon and alloying elements. M_s temperature is highly sensitive to the precise chemical composition of austenite, with minor deviations in C or substitutional element content causing substantial changes in the transformation temperature. In 30CrMnSi steel, this issue is further intensified by the presence of carbide-forming elements such as Cr. Austenitizing treatments might not fully dissolve carbides or cause segregation, resulting in a mismatch between the nominal and effective matrix composition. This composition gap explains why even advanced ML models that rely solely on nominal values struggle to achieve higher accuracy for M_s prediction.

Deeper integration of thermodynamic modeling and experimental microanalysis into data-driven frameworks could help address this limitation. For example, future models may use effective austenite composition, estimated by thermodynamic calculations or measured using techniques such as electron probe microanalysis (EPMA), to replace or supplement nominal composition as an input feature. In addition, including M_s values calculated from empirical formulas as an auxiliary feature would allow a ML model to learn systematic residuals and thus combine empirical knowledge with data-driven insight. Such hybrid approaches would substantially increase the fidelity and reliability of phase transformation predictions, especially for complex alloy systems and key transformation points such as M_s.

Moreover, it should be emphasized that the present study’s training and test data were derived from the same collection of literature CCT curves, with each data point intrinsically linked to its parent curve, steel grade, and source publication. While the random 7:3 split adopted in this work enables evaluation of fitting and prediction within the known data scope, it cannot rule out information overlap between the training and test sets. Stricter validations confirmed that the model’s extrapolation capability to entirely new steel grades remains limited. Future efforts will focus on enlarging the database with more diverse and independent CCT curves, incorporating physical constraints, and exploring nested validation to enhance model generalizability.