In ML, a feature represents an independent, observable attribute or characteristic of an observed object, and multiple features collectively form a feature vector. The dataset used in this work was derived from the data of a previous study^[57], underwent certain processing steps, and ultimately comprised experimental data points. To comprehensively consider feature parameters related to dynamic performance and enhance model interpretability, both material composition information and key domain knowledge were employed to generate features during database construction. Consequently, a comprehensive multi-component high-entropy alloy database containing 23 features was developed.

The raw data collection included both dynamic compression and dynamic tension records from the literature, totaling 312 data points. Since the present study focuses exclusively on dynamic compressive properties, all tension records (64 data points) were objectively excluded; no further filtering based on performance values or trends was applied. The final database therefore comprises 248 data points (compression only), covering 51 unique RHEA compositions from 46 source publications. All 248 records contain complete information for both dynamic yield strength and fracture strain, yielding 248 yield-strength and 248 fracture-strain records. Among these 248 records, 159 (≈ 64%) correspond to the as-cast state, which is the processing condition of primary interest for the present work; the remaining 89 (≈ 36%) records include thermomechanically processed or annealed states. The database covers strain rates from 400 to 6,000 s^-1, with dynamic yield strengths ranging from approximately 500 to 2,500 MPa and fracture strains varying between 5% and over 60%. Although some source publications (listed in Supplementary Table 1) reported test conditions extending beyond 6,000 s^-1, the specific compression records extracted from those publications and included in the present training database are all within the 400-6,000 s^-1 range. No additional performance- or trend-based filtering was applied beyond the objective exclusion of dynamic tension records (64 data points), as noted above. The compositional space encompasses 18 elements, including refractory metals (W, Mo, Hf, Ta, Nb, Zr), transition metals (Ti, V, Cr, Fe, Co, Ni, Cu, Mn), the light element Al, the non-metallic elements (Si, O), and minor additions of the rare-earth element Gd.

The domain-knowledge features employed in this work, including shear modulus (G), thermal conductivity (λ), Young’s modulus (E), Pugh’s ratio (B/G), and strain rate, were adopted from a prior investigation on knowledge-enabled ML for dynamic properties of high-entropy alloys^[57]. The formulas and calculation methods for these physical descriptors are summarized in Table 1. These descriptors are intended as heuristic indicators of the underlying physical tendencies (e.g., ductile-brittle character or thermal transport behavior) and are evaluated collectively through the predictive performance of the ML models. The selection of these features reflects the physical linkage to the three core mechanisms governing dynamic mechanical behavior: dislocation motion resistance, adiabatic heating, and ductile-brittle transition. Rather than performing exhaustive feature engineering, the present work focuses on systematically evaluating three feature strategies (composition-only, knowledge-only, and fusion) and embedding the optimal models into a multi-objective optimization framework with experimental validation.

Genetic algorithms are employed for multi-objective optimization of alloy composition. In this framework, each candidate alloy composition is encoded as an individual, and crossover and mutation operations directly modify the elemental fractions to generate new candidates. The algorithm iteratively searches the composition space guided by the objective function values evaluated by the ML models.

The simplest method to train models based on this principle is to use composition directly as the feature parameter. After crossover and mutation, these compositional features are normalized and then directly employed to train and optimize the model. The advantage of this approach is that it simplifies the program flow and reduces code complexity. The selection of domain-knowledge features (e.g., shear modulus, Pugh’s ratio) was guided by established empirical knowledge and phenomenological constitutive models related to dynamic deformation mechanisms, as evidenced in prior work^[57]. These physically meaningful descriptors, which have demonstrated effectiveness in correlating with mechanical properties, were adopted in the present study to construct interpretable models within the multi-objective optimization framework.

Therefore, the domain knowledge features used therein can be directly referenced to establish multi-objective optimization models. Throughout the optimization process, the genes of each individual remain the elemental composition. After a new individual is generated by crossover and mutation of the composition, predefined formulas are used to calculate the domain knowledge features of this individual, followed by the multi-objective optimization workflow. In this context, ML models are trained using three distinct feature compositions: composition features alone, domain knowledge features alone, and a fusion of both. The feature vectors correspondingly consist of “composition”, “domain knowledge”, or a combination of both. Since expert domain knowledge features are incorporated, this approach provides interpretability for the multi-objective optimization model. In summary, when conducting multi-objective optimization using these three methods, the genes constituting the alloy individuals remain the elemental composition of the alloy. However, the input–output mapping of the ML models differs across the three strategies: from composition only, from domain knowledge only, or from the fusion to the prediction target(s).

The present work does not aim to discover new physical descriptors through exhaustive feature engineering, as reported in recent titanium alloy studies^[59]. Instead, established domain-knowledge features, shear modulus (G), thermal conductivity (λ), Young’s modulus (E), Pugh’s ratio (B/G), and strain rate, derived from the prior investigations on the dynamic deformation of high-entropy alloys, are built upon^[57]. These features are physically linked to dislocation motion resistance, adiabatic heating, and ductile-brittle transition, the three core mechanisms governing dynamic mechanical behavior. The contribution of the present work lies in systematically evaluating three feature strategies, namely composition-only (C), knowledge-only (K), and composition + knowledge (CK), across eight ML algorithms and two target properties, and in embedding the optimal models into a multi-objective optimization framework with experimental validation.

As summarized in Figures 2 and 3, the CK fusion model generally achieves superior predictive performance compared to the C-only and K-only strategies, particularly for the more competitive ensemble algorithms such as ExtraTrees, Random Forest, and GradientBoosting. For instance, in dynamic yield strength prediction, the CK-ExtraTrees model achieves a test R² of 0.883 with root mean square error (RMSE) = 196 MPa, outperforming the best C-only model (R² = 0.834, GradientBoosting) and the best K-only model (R² = 0.777, random forest). However, CK is not universally dominant across all algorithms; for weaker learners such as KNNs and decision tree, the performance differences among the three feature strategies are marginal and inconsistent. Nevertheless, since the ExtraTrees algorithm with the CK feature set yields the highest predictive accuracy among all evaluated models, it is selected as the optimal model for subsequent hyperparameter optimization and multi-objective integration. This focused selection ensures that the best-performing combination, rather than a universally superior strategy, drives the downstream optimization.

These contrasting rankings carry significant implications. For strength prediction, composition-only models perform reasonably well (R² ≈ 0.83), whereas in the titanium alloy system reported by Liu et al.^[59], composition-only models yielded substantially lower performance (test R² ≈ 0.12 for strength). This discrepancy originates from the more direct correlation between elemental composition and strengthening effects in refractory multi-principal element alloys. In WW-RHEAs, the significant atomic size differences among constituent elements (W, Mo, Fe, Ni, etc.) are known to contribute to solid-solution strengthening, making composition a reasonably effective predictor for yield strength. For ductility prediction, however, composition-only models fail (R² ≈ 0.40), while knowledge features substantially improve performance (R² ≈ 0.57). This disparity indicates that fracture strain under dynamic loading is governed by complex, synergistic mechanisms, dislocation motion, adiabatic heating, and phase stability, that are better captured by physically meaningful descriptors than by raw composition alone.

Based on the systematic evaluation of the three feature strategies, the ExtraTrees algorithm with the CK fusion feature set was selected as the optimal model for both strength and ductility predictions. To further enhance performance and ensure robust generalization, hyperparameter optimization was conducted using a grid search strategy combined with five-fold cross-validation. The parameter space, including n_estimators, max_depth, and min_samples_split, was systematically explored, with the combination yielding the lowest cross-validation error selected for the final model.

The optimized ExtraTrees model for dynamic yield strength achieves a test R² of 0.96 with RMSE = 120 MPa [Figure 2D]. For fracture strain, the optimized model achieves a test R² of 0.87 with RMSE = 6.21% [Figure 3D]. The comparatively lower performance for ductility prediction reflects the inherently higher stochasticity of fracture strain under dynamic loading, which is governed by a complex interplay of dislocation motion, adiabatic heating, and crack initiation, mechanisms that are more challenging to capture from compositional and physical descriptors alone.

The convergence curves of test RMSE with respect to the ensemble size [Figure 2C and 3C] further confirm model robustness. Both models exhibit rapid convergence, with the test error stabilizing after approximately 50 decision trees and remaining flat as the tree count increases. This flat trend indicates that further increasing the number of trees does not introduce overfitting, suggesting that the hyperparameter-optimized ExtraTrees models have learned stable patterns within the sampled data domain, though the record-level random split does not guarantee generalization to entirely unseen compositions or processing conditions.

To move beyond “black-box” predictions, SHAP analysis was performed to quantify the contribution of each feature to the model predictions and to assess whether the model behavior aligns with established physical principles. It is important to emphasize that statistical associations within the trained model are revealed by SHAP values, and physical causality is not independently established by SHAP values. The following interpretations are therefore offered as model-consistent hypotheses that warrant further experimental and theoretical verification.

Strength model [Figure 2E and F]: Shear modulus (G) emerges as the dominant feature, with a mean |SHAP| value of 342.6. Samples with high G are concentrated in the positive SHAP region, which is qualitatively consistent with the greater resistance of high-modulus alloys to shear deformation. However, G is a composition-weighted average and is not a direct descriptor of local lattice distortion. The SHAP-derived association should therefore be interpreted as a model-based correlation with elastic stiffness, not as direct evidence of a specific strengthening mechanism. Thermal conductivity ranks second (mean |SHAP| = 143.6): samples with low thermal conductivity cluster in the positive region, indicating that reduced heat dissipation may facilitate localized thermal softening, while within the studied strain-rate regime it may also contribute to strain-rate hardening by limiting dynamic recovery; the net effect depends on the competition. It is recognized that under near-adiabatic high-rate loading, low thermal conductivity may also promote thermal softening and strain localization. The net effect on flow stress depends on the competition among strain hardening, strain-rate strengthening, and thermal softening. The SHAP-derived association should therefore be interpreted as a model-based trend rather than a definitive mechanistic conclusion. Strain rate ranks third (mean |SHAP| = 96.9), which is consistent with the expected positive strain-rate sensitivity of flow stress in dynamic compression, although this trend is model-derived and does not independently confirm a specific hardening mechanism.

Notably, compositional features such as Cr, Ni, and Al also show substantial contributions, with mean |SHAP| values of 44.1, 26.5, and 25.7, respectively. Cr exhibits a narrow-band positive distribution, which is consistent with a stable linear strengthening contribution, possibly related to solid-solution effects. Ni and Al show more distributed patterns: the effect of Ni is concentration-dependent, while Al exhibits an olive-shaped distribution, suggesting an optimal compositional window beyond which excessive Al may promote brittle phase formation. Hf (mean |SHAP| = 19.8) and O (mean |SHAP| = 15.7) also contribute meaningfully: the contribution of Hf may be associated with its large atomic radius and the resulting lattice distortion, although this interpretation remains model-derived and requires further experimental verification, and O contributes through interstitial strengthening, although Hf was subsequently excluded from the optimization system due to cost considerations. This result is consistent with the necessity of retaining compositional features in the strength model, a finding that distinguishes this work from titanium alloy systems where composition-only features were reported to be substantially less effective. The feature importance ranking suggests that both electronic-structural descriptors (G, thermal conductivity) and compositional identity show strong associations with accurate strength prediction in RHEAs.

Ductility model [Figure 3E and F]: Strain rate is the most influential feature (mean |SHAP| = 7.47), suggesting a strong association with fracture strain under dynamic loading. Fe and Co follow with mean |SHAP| values of 2.21 and 1.76, respectively. Notably, Young’s modulus (E) (mean |SHAP| = 1.07) and B/G (mean |SHAP| = 0.69), the classic Pugh’s ductile-brittle criterion, appear as key physical descriptors. High B/G values are concentrated in the positive SHAP region, suggesting that when B/G exceeds the critical threshold, shear deformation may become energetically more favorable, which is in line with the classical Pugh criterion but should be interpreted as a model-derived association. Young’s modulus shows an olive-shaped distribution: samples with moderate E cluster in the positive region, suggesting that excessively high E suppresses dislocation nucleation, while low E reduces the elastic energy storage capacity required for sustained plastic deformation.

Hf (mean |SHAP| = 0.79) and Al (mean |SHAP| = 0.59) also contribute to ductility predictions. The SHAP contribution of Hf may be associated with its strong lattice distortion effect, which can promote uniform deformation by activating multiple slip systems. Al exhibits a negative correlation in the swarm plot: samples with high Al content cluster in the negative SHAP region, suggesting an embrittlement risk at elevated Al concentrations, consistent with its tendency to promote ordered intermetallic formation. Compositional features such as Fe and Co exhibit bimodal distributions, indicating that the effects on ductility depend on specific alloying synergies rather than monotonic linear behavior. The SHAP results show that ductility predictions are strongly associated with knowledge features, particularly strain rate, Young’s modulus, and B/G, suggesting that these physically meaningful descriptors are useful for capturing the complex interplay of deformation mechanisms under dynamic loading. While individual physical descriptors each capture distinct mechanisms (e.g., B/G for brittle-ductile tendency, Young’s modulus for elastic energy capacity, thermal conductivity for adiabatic heating), the compositional features remain essential for resolving the non-uniqueness problem in the composition-to-descriptor mapping.

The SHAP analysis suggests two key trends: (i) knowledge features show strong associations with ductility prediction, while composition-only features show substantially weaker associations in this model; and (ii) compositional features show strong associations with strength prediction in RHEAs, reflecting the dominant role of solid-solution strengthening effects associated with compositional variations. This mechanism-dependent importance of feature selection underscores that no single “universal” feature strategy exists, the optimal approach must be tailored to the target property and alloy system. The knowledge-enabled interpretability of the model offers physically plausible hypotheses for the subsequent multi-objective search, potentially steering optimization toward regions that are not only performant but also interpretable in terms of established materials-science principles.

Based on the SHAP analysis in Section “SHAP analysis: model-based feature importance and physically plausible interpretations”, which identified Cr, Ni, and Al as significant contributors to strength, and Fe, Co, and Hf as influential for ductility, a virtual compositional space was defined for multi-objective optimization. The optimization was designed as a joint search over composition and loading condition, reflecting the fact that strain rate is an intrinsic service parameter in dynamic impact applications. The feature importance rankings, along with elemental frequency, price, and density distributions within the dataset [Figure 4], were used to guide the subsequent selection and exclusion of elements. To ensure both physical relevance and practical fabricability, the following constraints were imposed: (i) Hf was excluded due to its high cost, despite its substantial SHAP contribution to both strength and ductility; (ii) Al was eliminated because its excessively high melting point difference with W may increase the risk of segregation and element loss during arc melting; and (iii) W and Mo were mandatorily retained to favor high-density candidate designs. This yielded a nine-element search space comprising Ti, Cr, Fe, Co, Ni, Zr, Nb, W, and Mo, with atomic fractions for each element bounded between 0 and 35 at.%, and the strain rate ranging from 0 to 5,000 s^-1 [Table 2]. The objective functions were defined as maximizing both dynamic yield strength and fracture strain, subject to the constraint that all compositions sum to unity.

To evaluate the impact of different feature strategies on optimization outcomes, the NSGA-II algorithm was driven by predictive models trained on three distinct feature sets, composition-only (C), knowledge-only (K), and composition + knowledge (CK), to generate the respective Pareto frontiers.

As shown in Figure 5, the three strategies yield markedly different Pareto fronts. The K-only model produces an excessively homogeneous set of Pareto solutions, because the lower-dimensional physical feature space, compared to the vast compositional space, often leads the algorithm to associate “optimal” performance with a narrow range of physical parameters, while the reverse mapping to composition is non-unique and may not be practically realizable. The C-only model yields a broader Pareto front in the performance space, yet its “black-box” nature obscures the physical rationale behind the predicted properties, resulting in a lack of interpretability. In contrast, the CK fusion model achieves the optimal balance: it generates a high-quality Pareto solution set covering a wide range in both strength and ductility while, by virtue of the domain-knowledge features, associating each optimal composition with physically meaningful descriptors such as shear modulus and B/G. This approach unifies the breadth of data-driven exploration with the depth of physical knowledge.

Elemental distribution trends within the CK-derived Pareto front [Figures 6 and 7] reveal the compositional evolution underlying the strength-ductility trade-off. As alloys shift from the high-ductility region to the high-strength region (i.e., with increasing yield strength), the concentrations of elements such as Cr, Fe, Co, and Ni generally decrease, whereas the proportions of Ti, W, Mo, Nb, and Zr increase or remain high. This observed compositional pattern is qualitatively consistent with the expected roles of refractory elements in solid-solution strengthening, but direct mechanistic confirmation (e.g., via phase analysis or electron microscopy) is beyond the scope of the present optimization study. The Pareto front visually demonstrates the competition and compromise between these two categories. Notably, W and Mo appear with high frequency across all Pareto solutions, directly satisfying the pre-defined high-density constraint and indicating the effectiveness of the optimization framework in translating application requirements into compositional preferences. Simultaneously, strain rate within the optimal solution set is predominantly concentrated near 5,000 s^-1, aligning with the general principle of strain-rate hardening in dynamic compression.

This compositional trend analysis guided the convergence of the optimization system from the initial nine-element space toward the W-Mo-Fe-Ni quaternary system [Figure 8]. While the Ti-W-Mo-Nb-Zr system is capable of achieving excellent strength-ductility synergy, the W-Mo-Fe-Ni system offers superior ductility potential at considerable strength levels, and its simpler composition, coupled with the reported potential^[3] of W-heavy alloys for kinetic-energy penetrators, though this aspect is beyond the scope of the present dynamic-compression study, lays the groundwork for subsequent application-oriented investigations. The convergence to this system, however, introduces a fabricability challenge: the vast melting-point difference between W/Mo and Fe/Ni constitutes an inherent barrier for conventional arc melting, motivating the introduction of composition constraints in the iterative optimization that follows.

To address the fabricability challenge while preserving search efficiency, a master alloy strategy was adopted as a hard constraint within the NSGA-II framework. The strategy imposes equiatomic ratios between element pairs with similar melting points: Fe:Ni = 1:1 and W:Mo = 1:1. This facilitates practical fabricability by allowing a two-step process, pre-melting homogeneous Fe-Ni and W-Mo master alloys separately, followed by final co-melting, which reduces the melting-point mismatch between constituent elements without compromising compositional search efficiency. The optimization was then performed in three iterative rounds with progressively refined exploration strategies [Figure 9]. In each iteration, the NSGA-II algorithm systematically screened 250,000 objective evaluations on hypothetical compositions (with a population size of 500 and 500 generations).

First iteration: identifying the fabricability bottleneck. With the equiatomic constraints imposed, the NSGA-II algorithm conducted an initial screening over the W-Mo-Fe-Ni composition space. The resulting Pareto-optimal solutions were overwhelmingly concentrated in the ultra-high W-Mo regime, where the total atomic fraction of W and Mo, defined as the sum of the W and Mo atomic fractions, exceeded 60 at.%.

While these compositions exhibited excellent predicted mechanical properties, experimental realization of such compositions posed significant challenges: the extremely high melting point and limited mutual solubility between W/Mo and Fe/Ni at such concentrations may lead to practical fabrication challenges, such as segregation, incomplete melting, and element loss during arc melting. This outcome highlighted a critical gap between computational prediction and experimental feasibility, motivating a targeted exploration of lower W-Mo regions in subsequent iterations.

Second iteration: screening in the moderate W-Mo regime. Guided by the first iteration, the optimization search was redirected toward the moderate W-Mo optimization target range (20-50 at.%). The Pareto-optimal solutions from this iteration converged to a well-distributed front covering the entire 20-50 at.% W-Mo range. Five representative compositions with total atomic fractions of W and Mo of 20, 26, 34, 42, and 50 at.% (optimization targets), spanning the full Pareto front, were selected as candidates for experimental validation. During synthesis, the final two compositions were adjusted to nominal values of 41 and 49 at.% [see Section “Validation in the moderate W-Mo regime (nominal total atomic fraction of W and Mo ≤ 49 at.%)”]. Density, calculated using the formula in Table 1, was incorporated as a screening criterion in the NSGA-II optimization (with a threshold of 10 g/cm³); individuals with estimated density below this threshold were excluded from the Pareto front during the non-dominated sorting step (Section “Establishment of multi-objective optimization algorithm”). Subsequently, densities were measured for a subset of the synthesized alloys (Section “Experimental validation”, Table 3) to assess consistency with this screening criterion.

Third iteration: exploring the boundary of reliable prediction. To further probe the predictive capability along the same Fe:Ni = W:Mo pathway beyond the trained composition range, a third iteration targeted the W₃₀Mo₃₀Fe₂₀Ni₂₀ composition (total atomic fraction of W and Mo = 60 at.%), a representative Pareto-optimal candidate at the boundary with a high total atomic fraction of W and Mo of the explored design space identified in the first iteration.

The experimental validation of both the second-iteration candidates and the third-iteration boundary composition is presented in Section “Experimental validation”, where the predictive reliability of model in the well-predicted compositional regime and its limitations at the boundary of reliable prediction are systematically examined.

Five representative compositions with total atomic fractions of W and Mo of 20, 26, 34, 41, and 49 at.% (nominal synthesis compositions) were selected as candidates for experimental validation. The NSGA-II optimization initially identified targets of 42 and 50 at.%; the final two compositions were adjusted to nominal values of 41 and 49 at.% during weighing for synthesis. No post-casting compositional analysis [e.g., energy-dispersive X-ray spectroscopy (EDS) or inductively coupled plasma (ICP)] was performed; the reported compositions are therefore nominal values based on the weighing masses. All these compositions follow the same equiatomic ratio pattern (Fe:Ni = 1:1, W:Mo = 1:1) as the training data, providing a controlled compositional pathway for evaluating extrapolation along fixed Fe:Ni and W:Mo ratios, while progressively increasing the total atomic fraction of W and Mo beyond the training range (predominantly distributed between 10-35 at.%). All five as-cast alloys were successfully fabricated via the two-step master-alloy melting route.

Table 3 lists the measured densities of four selected candidate alloys; the 49 at.% alloy was measured but excluded due to excessive uncertainty. The values show a monotonic increase with the total atomic fraction of W and Mo: 9.95 g/cm³ at 20 at.%, 10.27 g/cm³ at 26 at.%, 10.64 g/cm³ at 34 at.%, and 11.30 g/cm³ at 41 at.%. Within this measured subset, compositions with a total atomic fraction of W and Mo ≥ 26 at.% exceed the 10 g/cm³ estimated-density screening threshold adopted in this study. This indicates that the density constraint can be satisfied within the moderate W-Mo regime while remaining synthesizable by conventional arc melting.

Figures 10 and 11 compare the experimental dynamic mechanical properties against the CK-fusion model predictions across a range of strain rates. Because systematic fracture evidence was not available for all specimens, all strain measurements are conservatively reported as ε_max (maximum compressive strain attained before unloading) rather than as true fracture strain. Conventional relative errors cannot be computed for strain; instead, a conservative consistency check (ε_f ≥ ε_max) is applied.

For yield strength, where measurements are fully observed, the individual relative prediction errors are evaluated. Within the tested regime of the nominal total atomic fraction of W and Mo ≤ 49 at.%, the CK-fusion model provides partial directional guidance: the predicted strength trend is broadly consistent with the experimental trend, but the individual prediction errors are non-negligible and tend to increase with increasing total atomic fraction of W and Mo. For strain, because the experimental values are right-censored lower bounds, a conservative consistency check (ε_f ≥ ε_max) is applied. In this regime, a subset of predictions satisfies the consistency criterion, but this reflects the conservative nature of the check rather than quantitative accuracy, because the model tends to predict high fracture strains while the measured ε_max values are lower bounds. Because the strain observations are right-censored, a rigorous joint quantitative accuracy rate for both objectives cannot be defined from the present experiments. Overall, within this moderate regime, the model captures the general trade-off trend and successfully guides the identification of high-density candidates that are more compatible with conventional arc melting.

To further probe the extrapolation behavior of the current model along the same composition pathway, the third iteration targeted the nominal W₃₀Mo₃₀Fe₂₀Ni₂₀ composition (total atomic fraction of W and Mo = 60 at.%), a boundary with a high total atomic fraction of W and Mo composition of the explored design space that lies beyond the better-sampled compositional regime established in the second iteration. This composition follows the same equiatomic ratio pattern (Fe:Ni = 1:1, W:Mo = 1:1) as both the training data and the second-iteration alloys. The prediction failure is therefore consistent with extrapolation beyond the training distribution, though microstructural changes at this extreme composition may also contribute. At this composition with a high total atomic fraction of W and Mo, which lies at the edge of the training-data distribution used to train the model, the underlying microstructure may undergo regime transitions, such as intermetallic precipitation or compositional segregation, that are not captured by the current feature set, which lacks microstructural descriptors.

As shown in Figure 12, the model predictions exhibit significant deviations from experimental values at this composition. For yield strength [Figure 12A], the ML-predicted values are consistently lower than the experimental results, indicating clear under-prediction. For strain [Figure 12B], because the experimental values are right-censored lower bounds (ε_max), cases with ε_f ≥ ε_max cannot be interpreted as quantitative over-prediction of the true fracture strain; these cases are only consistent with the observed lower bound. Only cases with ε_f < ε_max constitute definite under-prediction. At 2,054 s^-1, for example, the model predicts 14.5% while the specimen reached 25.0% before unloading, demonstrating a clear boundary failure for the strain target. The different deviation directions for the two properties may suggest that the current feature set does not fully capture the distinct physical mechanisms governing each property at extreme W-Mo concentrations, but this interpretation requires further microstructural investigation. The boundary results presented here were obtained within a single experimental campaign and do not establish batch-to-batch reproducibility. Independent melt-batch validation will be required before generalizing the quantitative response of this composition.

This boundary exploration reveals a fundamental distinction: the MMOS framework successfully converged to a promising composition region (W₃₀Mo₃₀Fe₂₀Ni₂₀) where attractive dynamic properties emerge in the as-cast state, even though this specific composition lies outside the reliable prediction domain of the model. The utility of the framework in this regime therefore derives primarily from its exploration efficiency, namely the ability to sample and converge on promising regions, rather than from composition-level prediction accuracy for every individual composition.

At a strain rate of 2,054 s^-1, the W₃₀Mo₃₀Fe₂₀Ni₂₀ as-cast alloy achieved a dynamic compressive yield strength of 2,174 MPa coupled with a maximum compressive strain of 25% [Figure 13A]. Figure 13A provides a qualitative benchmark against selected reported RHEAs from the literature under broadly comparable high-strain-rate conditions. The comparison indicates that the designed alloy falls within the upper-right region, exhibiting a strength-ductility balance that is broadly comparable to many reported RHEAs. It is acknowledged that the strain rates of the literature data are not perfectly identical to the testing conditions, typically ranging from ~10³ to ~5 × 10³ s^-1. Notably, the alloy achieves 2,174 MPa at a lower strain rate (2,054 s^-1) than several literature data points (> 4,000 s^-1). This suggests that the alloy compares favorably with the selected literature data, although a direct quantitative comparison is complicated by differences in testing conditions, microstructure, and processing history. The key conclusion remains that the MMOS framework successfully identified a composition with an attractive dynamic-compression response. The engineering stress-strain curves [Figure 13B] further reveal a pronounced work-hardening response prior to unloading, which is qualitatively consistent with the activation of effective deformation mechanisms under dynamic loading; however, the specific mechanisms require systematic microstructural characterization in future work.

First, despite the prediction failure at the 60 at.% W-Mo boundary, the multi-objective optimization framework successfully navigated the vast compositional space to identify an as-cast composition with a high total atomic fraction of W and Mo where attractive dynamic properties emerge directly after solidification. The value of the framework therefore lies not solely in prediction accuracy, but more fundamentally in its exploration efficiency, the ability to efficiently sample and converge on promising regions of the performance landscape, even at the limits of model reliability. Second, the observed prediction failure clearly delineates the applicability domain of the current model, providing a concrete direction for future improvement: incorporating quantitative microstructural descriptors (e.g., phase fraction, grain size, precipitate morphology) and expanding the training database into the under-sampled region beyond a total atomic fraction of W and Mo of 50 at.% are essential for extending the applicability of the framework. Third, this work establishes a foundation for future closed-loop development by completing the first complete design-and-validation cycle. The experimental data generated at the boundary of the model, including both the experimentally characterized cases in the nominal total atomic fraction of W and Mo ≤ 49 at.% tested regime and the systematic deviations observed at total atomic fraction of W and Mo = 60 at.%, have not yet been used to retrain and prospectively retest the model, as such an iterative cycle lies beyond the scope of the present study. However, these data have been archived as an experimental feedback dataset for future incorporation into an expanded training database and provide the basis for the subsequent iteration of model refinement. This progressive accumulation of empirical feedback, building toward a fully closed-loop paradigm, provides the basis for future refinement of the framework. The present work reports a complete design-and-validation cycle, from computational screening to SHPB validation, establishing a foundation for future closed-loop development, while delineating the current limitations of the framework.