Page 257 - Read Online

Page 22 of 29 Liu et al. J. Mater. Inf. 2026, 6, 18

ductility and highlighting its intrinsic value for assessing material ductility. Titanium content exhibits an
olive-shaped nonlinear distribution, with low titanium concentrations densely clustered in the negative
SHAP region and high titanium concentrations concentrated in the positive SHAP region. This pattern
reveals an optimal concentration window for titanium in high-performance titanium alloys. The mixing
enthalpy exhibits clear monotonic behavior. Negative values indicate strengthened atomic bonding,
enhancing ductility, whereas positive values correspond to weakened bonding capacity, reducing
deformability and ductility. Notably, traditional alloying elements Mo and Si exert minimal influence, while
samples with high Al content cluster in the negative SHAP region, suggesting embrittlement risks. Zr
exhibits neutral effects, while the influence of Fe is highly dependent on compositional synergies. Swarm
plots further reveal a critical threshold effect for strain rate: high strain rates enhance ductility through
dislocation slip, while low strain rates cause embrittlement due to dislocation pile-up. Deviations from the
optimal titanium concentration promote brittle phase formation. Collectively, these patterns prove that
optimizing ductility requires avoiding embrittlement thresholds while precisely controlling the
composition-process synergy.

To rigorously assess the reliability of the ML models, particularly under high strain rate conditions, the
predictive uncertainty for both impact strength (GBRT model) and ductility (RF model) was quantified. The
test data were categorized into three regimes based on strain rate: Low (< 2,000 s ), Medium (2,000-4,000 s ),
-1
-1
and High (> 4,000 s ). The prediction results with 95%CIs (estimated via quantile loss for GBRT and
-1
ensemble variance for RF) are illustrated in Figure 15. In the Medium regime (2,000-4,000 s ), which
-1
encompasses the target design strain rate of 3,000 s , the strength model demonstrates excellent agreement
-1
between predicted and experimental values, with minimal uncertainty. The ductility model, reflecting the
inherently higher stochasticity of plastic deformation, shows wider CIs but still effectively captures the
experimental data points. These results confirm that 3,000 s lies within the robust interpolation domain of
-1
the models. Conversely, in the High regime (> 4,000 s ), a marked increase in predictive uncertainty is
-1
observed for both properties, characterized by significantly wider error bars and larger residuals. This
quantitative evidence aligns with data scarcity under extreme conditions and justifies the design strategy
adopted in this work: by limiting the optimization target to 3,000 s , the risks associated with extrapolation
-1
are effectively mitigated, ensuring that the designed alloys are based on high-confidence predictions.

As illustrated in Figure 16A, the GBRT model demonstrates a healthy learning process, where the test error
decreases rapidly and stabilizes after approximately 100 iterations, showing no sign of divergence even as the
training error continues to decrease. Similarly, Figure 16B confirms the stability of the RF model, with the
test error converging quickly and remaining flat beyond 50 trees. The absence of an upward trend in the test
loss curves for both models indicates that they effectively capture the underlying composition-property
relationships without overfitting to noise, thereby ensuring strong generalizability.

Exploring the proto frontier using the NSGA-II model and conducting theoretical verification
The optimal strength and ductility prediction models, developed by integrating domain knowledge and alloy
composition, were incorporated into the NSGA-II multi-objective optimization framework. Design
constraints consistent with near-α titanium alloy equivalence criteria were imposed to identify alloy
compositions with superior performance at a strain rate of 3,000 s . As shown in Figure 17A, the explored
-1
population densely covers most of the feasible design space, while the population at the 500th generation
forms a distinct convex Pareto front, confirming the intrinsic strength-ductility trade-off in titanium alloys
and validating the predictive accuracy of the integrated models. Among the 228,516 alloy candidates
satisfying the imposed constraints, fourteen Pareto-optimal solution sets were identified [Table 8]. These
Pareto‑optimal alloys span a broad range of strength and ductility, reflecting different trade‑off preferences
along the Pareto front: some solutions favor maximum strength at the expense of ductility, while others