This study proposes an interpretable ML-assisted co-design strategy for heat-resistant cast aluminum alloys, with its overall workflow illustrated in Figure 1. Implemented on the Python Scikit-learn platform^[30], this framework primarily consists of six phases: data collection, feature construction and selection, model training and evaluation, GA optimization, SHapley Additive exPlanation (SHAP) interpretability analysis, and experimental validation. First, a foundational database is constructed by collecting data on alloy compositions, processing parameters, testing conditions, and ultimate tensile strength (UTS) of heat-resistant cast aluminum alloys from published literature. Subsequently, a descriptor set reflecting the physicochemical characteristics of the elements is constructed by combining alloy compositions with intrinsic elemental properties. To effectively reduce the dimensionality of the alloy design variables, an ML model is built using the selected features as inputs and UTS as the output, with its performance evaluated by the coefficient of determination (R²). Building upon this, a GA is coupled to co-design novel alloy compositions and heat treatment parameters. The SHAP interpretability method is then employed to quantitatively reveal the contribution of each key feature to the UTS. Finally, experimental fabrication and performance testing are conducted to validate the UTS of the designed alloys at 300 °C, and their heat-resistant strengthening mechanisms are systematically elucidated in conjunction with microstructural characterization.

Figure 3A illustrates the distribution of alloy compositional complexity within the UTS dataset. The samples predominantly consist of multicomponent systems containing between 1 and 13 alloying elements, excluding the Al matrix. This high degree of compositional diversity, coupled with the intricate combinations of alloying elements, significantly expands the informational landscape of the dataset. While this enhances the generalization capability of ML models for complex multicomponent systems, it simultaneously exacerbates the challenges associated with alloy optimization and mechanical property tailoring.

The dataset encompasses 32 distinct alloying elements, with their specific types and compositional distributions detailed in Figure 3B. Notably, La exhibits the broadest compositional range among the additions (0-19.38 wt.%), while the maximum contents of Si, Ce, Mg, Cu, and Ni all exceed 5 wt.%. Elements such as Mn, Er, Fe, Cr, and Zn are primarily distributed within the 1.0-5 wt.% range, whereas the remaining elements are largely concentrated below 1 wt.%. Guided by these distributions, the compositional search space was strategically defined to align with practical content ranges, thereby improving modeling efficiency and mitigating the computational burden of high-dimensional feature spaces.

Figure 3C presents the distribution of processing parameters. The dataset covers a broad spectrum of critical variables, including melting conditions, heat-treatment parameters (solution and aging temperatures/times), and tensile testing conditions. These parameters exhibit distinct distributions with wide spans, reflecting the diverse fabrication routes reported in the literature. Such extensive coverage facilitates the model’s ability to learn complex composition–process–property relationships, although it inevitably increases the dimensionality and nonlinearity of the feature space.

The distribution of UTS values with respect to testing temperature is shown in Figure 3D. The UTS ranges from 11 to 590 MPa across testing temperatures of 20-530 °C. Data collected at 25 °C constitute the largest fraction (~33.9%), with significant portions also at 250, 300, and 350 °C. Conversely, samples at other temperatures account for less than 10%. This distribution indicates that existing research has focused primarily on room and elevated temperatures, while data at the extremities of this temperature spectrum remain relatively scarce.

First, the Pearson correlation coefficient was employed to screen the initial feature set and eliminate multicollinearity between variables. Figure 4A presents the feature correlation heatmap after removing strongly correlated variables. This step ensures the independence of input variables, thereby reducing model redundancy and enhancing computational efficiency. Subsequently, feature contribution was evaluated based on the RF algorithm, with the top 15 features by importance score shown in Figure 4B. The results indicate that the testing temperature (Temp) has a decisive influence on the UTS of the alloy. Furthermore, the thermal exposure time before high-temperature tension (t-ten-hold) and the primary aging time (A1-t) also exhibited high importance. This reflects the significant impact of matrix recovery and precipitate coarsening induced by holding time at elevated temperatures on strength evolution. Given the compositional framework and service conditions of heat-resistant cast aluminum alloys, the Al content and testing temperature (Temp) were initialized as the baseline input features for the model. To determine the optimal feature subset, an exhaustive feature selection strategy was adopted, using R² from 10-fold cross-validation as the evaluation metric. As illustrated in Figure 4C, the model performance rises rapidly with the number of features before reaching a plateau. The performance peaks at 13 features (indicated by the red star). In Figure 4B, the pink bars represent the feature subset selected for the optimal model, while the blue bars represent excluded features whose inclusion would increase model complexity without significantly improving generalization capability. The UTS prediction results based on this optimal feature set are shown in Figure 4D. The experimental measurements and model predictions demonstrate high consistency, with R² values for the training and testing sets reaching 0.885 and 0.881, respectively. Additionally, the mean absolute error (MAE) for the testing set is 22.639 MPa, indicating that the model accurately captures the complex nonlinear mapping between temperature, composition, processing, physicochemical properties, and tensile strength. To further quantify the robustness of the model, 10-fold cross-validation was performed on the training set. The average cross-validation R² was 0.885 with a SD of 0.023, indicating stable predictive performance across different data partitions. The independent test set yielded an R² of 0.881, a root mean square error (RMSE) of 32.944 MPa, and an MAE of 22.639 MPa. Furthermore, the residual-based 95% prediction interval was estimated from the cross-validation residuals. The 2.5th and 97.5th percentiles of the residuals were -68.207 and 75.926 MPa, respectively. Therefore, for a predicted UTS value $$ \hat{y} $$, the empirical 95% prediction interval can be expressed as $$ \hat{y} $$ - 68.207 MPa to $$ \hat{y} $$ + 75.926 MPa. In addition, a benchmark comparison among ten representative regression algorithms was performed using the same feature subset and data partitioning, as summarized in Supplementary Information 3. RF exhibited the best overall balance among predictive accuracy, robustness, and generalization capability; therefore, it was selected as the final model.

Based on the established UTS prediction model, a co-design optimization of alloy compositions and processing parameters was performed. For the compositional design, Al was used as the matrix element, with four candidate alloying elements (Cu, Mg, Mn, and Ti) serving as design variables. To ensure physical consistency and data integrity, the sum of the mass fractions of these five elements was strictly constrained to 100%. On this basis, three heat treatment parameters (solution time ST1-t, artificial aging time A1-t, quenching temperature QT), three testing conditions (tensile temperature Temp, thermal exposure time t-ten-hold, tensile rate v), and two types of physicochemical descriptors (bulk modulus Bulk Prop. and covalent radius Cov. Prop.) were combined to systematically explore optimal combinations. The tensile rate was fixed at 0.06 mm/min. Given that the typical service temperature for piston alloys is approximately 300 °C^[34], the design temperature (Temp) was set accordingly to ensure alignment with actual engineering service conditions. Simultaneously, the thermal exposure time (t-ten-hold) was unified at 60 min. This setting is a widely adopted standard in high-temperature mechanical testing to minimize interference from transient thermal gradients and short-term microstructural instability, thereby improving the reliability and comparability of the model-guided UTS data. Physicochemical descriptors were dynamically calculated according to the method described in Section “Calculation of features”. The compositional search boundaries were defined according to the elemental concentration ranges covered by the experimental database, ensuring that GA optimization was performed within the data-supported domain of the trained ML model and avoiding unreliable extrapolation. Practical metallurgical constraints were also considered, since excessive alloying contents may promote microsegregation, coarse brittle intermetallic formation, hot tearing, and casting defects, thereby deteriorating castability and heat-treatment response. The specific search ranges and constraints for alloy compositions and heat treatment parameters are listed in Table 1, defining the boundary conditions for the GA optimization. Based on the GA optimization results, four alloys (labeled ZL-1, ZL-2, ZL-3, and ZL-4) were selected for experimental validation, with their compositions, processing parameters, and predicted performance summarized in Table 2.

As shown in Table 2, the absolute relative deviations between the predicted and experimental UTS values of the four designed alloys are 3.08%, 8.96%, 12.92%, and 0.46%, respectively, with an average deviation of 6.36%. These results indicate that the ML model can reasonably capture the general strength level of the designed alloys, although certain deviations remain. It should also be noted that the predicted UTS values are slightly lower than the corresponding experimental values for all four alloys, suggesting a certain degree of systematic underestimation. This discrepancy may be attributed to several factors. First, unavoidable experimental uncertainties may be introduced during alloy melting, casting, heat treatment, and tensile testing. Second, the measured alloy compositions differ slightly from the nominal compositions used for model prediction, which may affect the final mechanical properties. Third, the current model mainly considers alloy compositions and processing parameters, while microstructural factors such as phase fraction, precipitate size, grain-boundary phase distribution, and defect characteristics were not explicitly included as input descriptors. Therefore, although the model provides useful guidance for alloy and process design, further incorporation of additional experimental data and quantitative microstructural descriptors is expected to improve the prediction accuracy and generalization capability of the model.

The tensile properties of the designed alloys were experimentally tested at 300 °C and compared with two commercial cast aluminum alloys, ZL114A and ZL205A, as shown in Figure 5. The experimental results indicate that the ML-designed alloys significantly outperform the commercial alloys in terms of elevated-temperature strength. Among them, the ZL-2 alloy exhibits the highest UTS, reaching 214.2 MPa. Compared to ZL114A (133.0 MPa) and ZL205A (171.2 MPa), its strength increased by 61.0% and 25.1%, respectively. The ZL-3 and ZL-4 alloys also demonstrate excellent elevated-temperature strength, with UTS values of 205.1 and 194.9 MPa, respectively. In contrast, the tensile strength of the ZL-1 alloy is slightly lower at 181.6 MPa, which is primarily attributed to the presence of coarse primary intermetallic compounds within its microstructure.

To further benchmark the elevated-temperature tensile performance of the designed alloys, the UTS values at 300 °C were compared with those of previously reported heat-resistant cast aluminum alloys^[35-41], as summarized in Table 3. The present ML-designed gravity-cast alloys exhibit UTS values ranging from 181.6 to 214.2 MPa at 300 °C, which are higher than those of the representative gravity-cast heat-resistant aluminum alloys listed in the table. In particular, the ZL-2 alloy achieves a UTS of 214.2 MPa, exceeding not only the commercial cast aluminum alloys examined in this study but also the previously reported gravity-cast alloys tested at the same temperature. It is noteworthy that several squeeze-cast alloys were also included as broader benchmarks, because squeeze casting generally provides improved densification and is often beneficial for mechanical performance compared with conventional gravity casting. Even under this broader comparison, the UTS values of the present gravity-cast alloys remain higher than those of the listed squeeze-cast alloys. This result highlights the effectiveness of the ML-guided composition–process co-design strategy in developing heat-resistant cast aluminum alloys with superior elevated-temperature strength.

Regarding tensile ductility, traditional perspectives suggest that the introduction of thermally stable strengthening phases inevitably sacrifices material ductility, thereby leading to the typical strength-ductility trade-off^[42-46]. However, the alloys designed in this study maintain a certain degree of ductility while preserving high strength. Specifically, the elongation of the ZL-3 alloy is approximately 4.18%, which is higher than that of the commercial cast alloys. These results demonstrate that the ML-assisted design strategy is capable of significantly enhancing elevated-temperature strength while some compositions retain comparatively favorable ductility.

Table 4 lists the SDAS values measured from the as-cast optical micrographs of the investigated alloys, and the corresponding representative micrographs are presented in Supplementary Figure 2. The SDAS values of the ZL-1~ZL-4 alloys range from 21.24 to 27.02 μm, indicating relatively refined dendritic structures. Among them, ZL-2 exhibits the smallest SDAS, whereas ZL-3 shows the largest value within the ZL-1~ZL-4 alloy series. In comparison, ZL205A exhibits the largest SDAS among all the investigated alloys, corresponding to a coarser as-cast dendritic structure. These results demonstrate that the investigated alloys possess different as-cast solidification microstructures. SDAS is a characteristic parameter reflecting local solidification kinetics, dendritic refinement, and solute redistribution during casting. A smaller SDAS generally corresponds to a shorter interdendritic diffusion distance and a more refined dendritic framework, which may alleviate local microsegregation and promote more homogeneous solute redistribution in the as-cast matrix and during subsequent heat treatment. Therefore, SDAS measurement provides quantitative support for describing the initial casting microstructure and solidification characteristics of the investigated alloys.

It should be emphasized that SDAS is not the sole factor governing the elevated-temperature strength, but rather provides an important microstructural indicator for evaluating the initial solidification condition prior to heat treatment and precipitation. The relatively small SDAS of ZL-2 suggests a refined dendritic framework and shortened solute redistribution distance, which may facilitate a more uniform distribution of alloying elements during post-solidification heat treatment and provide a favorable microstructural basis for the subsequent formation of heat-resistant Al₂₀Cu₂Mn₃/Al₂CuMg-containing phases and nanoscale precipitates. This is consistent with the superior UTS of ZL-2 at 300 °C. In contrast, ZL-3 still exhibits high elevated-temperature strength despite having the largest SDAS among the designed alloys, indicating that the final strength is not determined by SDAS alone but by the combined effects of solidification microstructure, precipitation behavior, secondary-phase constitution, and phase distribution. Thus, the SDAS analysis serves as a quantitative microstructural complement to the machine-learning-guided composition–process design rather than an independent strength criterion.

Figure 6 shows the XRD results for each alloy. It can be observed that the characteristic diffraction peaks of Al₂₀Cu₂Mn₃ and Al₂CuMg are detected in ZL-2, ZL-3, and ZL-4, whereas the primary precipitate phase in ZL-1 is Al₂CuMg. In addition, Al₃Ti is detected in both the designed alloys and ZL205A; in contrast, the primary second phase in ZL114A is Mg₂Si. Figure 7 presents the representative SEM microstructural morphologies of the alloys. The numbered markers in the figures correspond to the EDS analysis locations, and the relevant results are summarized in Table 5. Combining the XRD and EDS analyses, the intermetallic compounds identified in the alloys primarily include Al₂₀Cu₂Mn₃, Al₂CuMg, Al₃Ti, Mg₂Si, primary Si, and eutectic Si.

As shown in Figure 7A, Al₃Ti in ZL-1 is mainly distributed intragranularly in a blocky or lath-like morphology, while Al₂CuMg predominantly precipitates at the grain boundaries as a fine dispersed phase. Figure 7B reveals that a large amount of Al₂₀Cu₂Mn₃- and Al₂CuMg-containing secondary phases/intermetallic phases are distributed along the grain boundaries of ZL-2; correspondingly, Al₂₀Cu₂Mn₃ and Al₃Ti phases can also be observed intragranularly. Compared with Figure 7B, the phase composition of ZL-3 in Figure 7C is fundamentally consistent, but the amount of intragranular Al₃Ti phase significantly increases, whereas the precipitation of Al₂₀Cu₂Mn₃ and Al₂CuMg at the grain boundaries decreases. ZL-4, shown in Figure 7D, exhibits an opposite trend: the amount of intragranular Al₃Ti phase decreases, while the precipitation of Al₂₀Cu₂Mn₃ and Al₂CuMg phases at the grain boundaries increases. In contrast, ZL114A in Figure 7E contains a large amount of Si-rich phases distributed continuously along the grain boundaries, while Figure 7F indicates that ZL205A mainly precipitates at the grain boundaries in the form of fine, discrete Al₃Ti particles.

As shown in Figure 8A, a high density of nanoscale precipitates is distributed in the Al matrix. The rod-like/plate-like precipitates in Figure 8B can be identified as Mn-rich Al₂₀Cu₂Mn₃ precipitates, as evidenced by the pronounced Mn and Cu enrichment in the corresponding STEM–EDS elemental maps. In contrast, the fine lath-like precipitates shown in Figure 8C are identified as Al₂CuMg precipitates, consistent with the enrichment of Cu and Mg. The corresponding indexed FFT patterns and lattice-fringe analyses are presented in Supplementary Figure 3. The HRTEM and inverse FFT images in Figure 8(B1, B2) and (C1, C2) further reveal clear lattice fringes within these precipitates and well-defined precipitate/matrix interfaces, indicating their crystalline nature and relatively favorable interfacial matching with the Al matrix. Such interfacial characteristics are beneficial for impeding dislocation motion and are expected to contribute to precipitation strengthening during elevated-temperature deformation. Statistical analysis shows that the average sizes of Al₂₀Cu₂Mn₃ and Al₂CuMg precipitates are 219.4 ± 119.0 nm and 109.8 ± 57.2 nm, respectively [Figure 8D and E]. Overall, two main types of nanoscale precipitates are observed in the ZL-2 alloy: relatively coarse rod-like/plate-like Mn-rich Al₂₀Cu₂Mn₃ precipitates and finer lath-like Al₂CuMg precipitates. The Mn-rich Al₂₀Cu₂Mn₃ precipitates are expected to provide thermally stable strengthening during elevated-temperature deformation, whereas the finer Al₂CuMg precipitates provide additional precipitation strengthening in the Al matrix. Therefore, the coexistence of these two types of nanoscale precipitates contributes to the superior elevated-temperature strength of the ZL-2 alloy.

Previous studies have shown that the key to enhancing the elevated-temperature strength of cast heat-resistant aluminum alloys lies in suppressing dislocation climb and grain boundary atomic diffusion at high temperatures^[47,48]. Complex intermetallic compounds distributed along grain boundaries can form relatively closed network-like or skeletal microstructures. Such microstructures facilitate the transfer of stress from the matrix to the strengthening phases and, to a certain extent, inhibit grain boundary sliding. Generally, the finer the second-phase particles and the more dispersed their distribution along the grain boundaries, the better the heat resistance of the alloy. It can be seen from Figure 7B that ZL-2 contains a relatively large amount of the Al₂₀Cu₂Mn₃ phase. Al₂₀Cu₂Mn₃ has been reported as a thermally stable Mn-rich strengthening phase in Al-Cu-Mn-based alloys, which can form during solidification and further precipitate as fine dispersoids during subsequent homogenization or solution treatment, thereby contributing to the enhanced thermal stability and elevated-temperature strength of Al alloys in the 300-350 °C range^[49,50]. Therefore, the abundant and relatively stable Al₂₀Cu₂Mn₃ phases in ZL-2, together with the Al₂₀Cu₂Mn₃/Al₂CuMg composite structures distributed at the grain boundaries, can more effectively suppress dislocation climb and grain boundary sliding during elevated-temperature tensile testing, thereby exhibiting superior high-temperature strengthening effects. From Figure 7C and D, it can be further observed that the amount of intragranular Al₃Ti phases in ZL-3 increases, while the amount of Al₂₀Cu₂Mn₃ and Al₂CuMg phases at the grain boundaries decreases. This causes its strengthening effect to rely more on intragranular dispersed phases, resulting in a lower elevated-temperature strength compared to ZL-2. In ZL-4, the precipitation of Al₂₀Cu₂Mn₃ and Al₂CuMg at the grain boundaries increases, leading to enhanced grain boundary strengthening. However, due to the reduced amount of the intragranular Al₃Ti phase, the intragranular support is insufficient, and the overall strengthening effect still fails to reach the level of ZL-2. ZL-1, shown in Figure 7A, is predominantly composed of Al₂CuMg and lacks the more thermally stable Al₂₀Cu₂Mn₃ phase. Since strengthening phases related to the Al-Cu-Mg system are more prone to coarsening and strength degradation at high temperatures, its elevated-temperature performance is relatively weaker^[51-53].

The microstructural characteristics of the commercial alloys are also consistent with the differences in their elevated-temperature performance. As shown in Figure 7E, a large number of Si-rich phases in ZL114A are continuously distributed along the grain boundaries. Such continuous grain boundary second phases weaken microstructural continuity. Moreover, its primary strengthening phase, Mg₂Si, easily coarsens and loses effectiveness above approximately 225 °C^[54]; therefore, it is difficult to maintain a stable strengthening effect under 300 °C conditions. In contrast, the fine, discrete Al₃Ti particles precipitating at the grain boundaries of ZL205A in Figure 7F contribute to improving grain boundary stability^[55,56]. However, due to the lack of a dominant heat-resistant phase with stronger thermal stability, its overall elevated-temperature strengthening effect remains limited. Overall, the elevated-temperature performance of the investigated alloys is governed by the coupled effects of the initial solidification microstructure, and the type, amount, morphology, and distribution of thermally stable secondary phases and nanoscale precipitates. This microstructural evidence supports the machine-learning-guided alloy design results, indicating that the superior UTS of ZL-2 at 300 °C arises from a favorable combination of refined solidification structure, stable Al₂₀Cu₂Mn₃/Al₂CuMg-containing phases, and nanoscale precipitation strengthening.

Since the RF model is a typical black-box model, relying solely on prediction accuracy is insufficient to reveal the actual contributions of individual input variables to the UTS. Therefore, this study further employs the SHAP method to interpret the model. Figure 9 presents the SHAP bee swarm plot (summary plot), where each feature is ranked according to its mean absolute SHAP value to characterize its global impact magnitude on the UTS prediction. It can be observed that Temp (temperature) is the primary factor affecting UTS. The SHAP values corresponding to high temperatures are mainly distributed in the negative region, while low temperatures mostly correspond to positive contributions, indicating that elevated temperatures significantly suppress UTS. This result is highly consistent with the fundamental metallurgical principles of matrix softening, the activation of dislocation motion, and the enhancement of grain boundary sliding at high temperatures. In addition to temperature, ST1-t, Ti, t-ten-hold, Cu, and Mg also exhibit high feature importance, indicating that heat treatment parameters and key alloying elements jointly dominate the strength evolution. Particularly, the prominent roles of Cu, Mg, and Ti correspond to the primary strengthening phases such as Al₂₀Cu₂Mn₃, Al₂CuMg, and Al₃Ti identified in Section “Phase constitution and microstructural characteristics”. This demonstrates a strong consistency between the key features extracted by the ML model and the microstructural strengthening mechanisms revealed by experiments. To further analyze the effect of key compositional features, Figure 10 presents the SHAP dependence plot of Cu, colored by Mn and Mg contents, respectively. As seen in Figure 10A and B, the contribution of Cu to the UTS exhibits obvious nonlinear characteristics. At low Cu contents, its SHAP values are generally low or even negative; as the Cu content increases, the SHAP values gradually turn positive and increase significantly, indicating that higher Cu contents are more conducive to improving the UTS. This trend implies that the strengthening effect of Cu is not linearly cumulative, but rather closely related to its capability to participate in the formation of effective strengthening phases. Furthermore, Figure 10 also indicates that the effect of Cu is synergistically modulated by Mn and Mg. Combined with the analysis in Section “Phase constitution and microstructural characteristics”, Mn participates in the formation of the highly thermally stable Al₂₀Cu₂Mn₃ phase, while Mg co-forms the Al₂CuMg phase with Cu. Therefore, the interactions between Cu–Mn and Cu–Mg possess a clear microstructural basis; that is, the contribution of Cu to the strength depends not only on its intrinsic concentration but also on whether it can synergistically promote the precipitation and stable distribution of heat-resistant strengthening phases. Among these, the synergistic effect of Cu-Mn is of vital significance for high-temperature strengthening because Al₂₀Cu₂Mn₃ possesses superior thermal stability, making it more effective at pinning and inhibiting dislocation climb and grain boundary sliding during high-temperature tensile deformation. Overall, the SHAP analysis indicates that the prediction of UTS by the RF model primarily relies on temperature, heat treatment processes, and key compositional variables such as Cu, Mg, and Ti. Furthermore, these highly important features align well with the phase constituents and microstructural evolution patterns obtained via experimental characterization. These results demonstrate that the established model not only possesses excellent predictive capability but also reflects, to a considerable extent, the underlying materials science principles governing the variations in the high-temperature strength of the alloys.