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Page 10 of 17 Cheng et al. J. Mater. Inf. 2025, 5, 53 https://dx.doi.org/10.20517/jmi.2025.61

different reference value each cycle. Nonetheless, the overall trend of HV increases with Pop size. When the
population reaches 200, the spacing decreases significantly, approaching nearly zero. Systematic evaluation
demonstrates that both convergence efficiency and solution quality in the inverse design model are
positively correlated with Pop size, with satisfactory stability achieved when the Pop size exceeds 300.

The effects of mutation and crossover probabilities are further examined, as illustrated in Figure 4B and C,
respectively. The findings indicate that at relatively low mutation probabilities, the model exhibits good
convergence and less impact on overall solution quality, as evidenced by fluctuations in the HV metrics at
higher levels. This suggests that the variations in mutation probability have a limited effect on the solution
quality, indicating that the solution obtained by the NSGA-II algorithm is in good agreement with the real
solution. When the mutation probability exceeds 0.5, the uniformity of the solution diminishes and the
stability is compromised. This indicates that the NSGA-II algorithm exhibits enhanced convergence
efficiency under lower mutation probabilities, resulting in optimization results that are closer to the true
values. Conversely, the variation of the crossover probability shows a negligible effect on all four indicators.
The HV value remains high and close to 1, while the GD and spacing values remain low. This indicates that
the quality of the solution set and the coverage of the objective space are maintained at an optimal level.

To enable computationally efficient alloy design, the optimization of Gen was systematically analyzed. The
number of selection, crossover, and mutation operations performed by the model increases with the
number of the Gen. It should be noted that configurations with inadequately low Gen may induce
insufficient exploration of the target space, and result in local optimization. As illustrated in Figure 4D, the
degrees of convergence, diversity, and uniformity of the model are markedly enhanced, while the stability of
the model is essentially maintained up to 300 generations. Consequently, the optimal parameter settings for
the Mg alloy inverse model are Pop size = 300, Mutation = 0.5, Crossover = 0.7, and Gen = 300.

In order to verify the design capability of the developed RF-NSGA-II framework, we applied the model to
alloy design using two different target properties as inputs: Alloy 1: UTS = 400 MPa; EL = 5% and Alloy 2:
UTS = 250 MPa; EL = 20%. Figure 5 illustrates the Pareto frontier optimization results for the two alloys. It
is clear that the non-dominated solutions obtained by the model show a relatively small error from the
target properties. Specifically, the non-dominated solutions for Alloy 1 show small deviations of less than
11 MPa and 0.07% from the target UTS and EL, respectively, while those for the high-ductility Alloy 2 show
deviations of 18 MPa and 8%, respectively. Based on the obtained non-dominated solutions, the optimized
solution can be determined using Equation (2). The chemical compositions and processing parameters
determined by the established inverse model are shown in Table 4 for Alloy 1 and Alloy 2.

To verify the predictions, the two designed Mg alloys are experimentally fabricated and processed according
to the chemical composition and processing parameters listed in Table 4. The experimentally measured
engineering stress-strain curves of both alloys are shown in Figure 6. The measured UTS and EL are
387 MPa and 4.4% for Alloy 1 and 259 MPa and 20.7% for Alloy 2, which are in excellent agreement with
the target mechanical properties. Figure 7 compares the experimental results with the predicted and target
values. Specifically, Alloy 1 exhibits deviations of ΔUTS = 13 MPa (~3.4%) and ΔEL = 0.6%, while Alloy 2
shows smaller deviations of ΔUTS = 9 MPa (~3.5%) and ΔEL = 0.7%. These results confirm the accuracy and
robustness of the established RF-NSGA inverse design model in predicting the mechanical properties of Mg
alloys.

Inverse design of high-performance Mg-Gd-based alloy
For data-centric ML methods, the ability to effectively guide high-performance alloy design at or beyond