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Li et al. J Mater Inf 2024;4:27 https://dx.doi.org/10.20517/jmi.2024.44 Page 9 of 20

GBR, KNR, and ANNR), and its predictive abilities were assessed through the hold-out method. The RMSE
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and R values of Model-III constructed by these algorithms are illustrated in Figure 3A. To reduce random
2
error, the RMSE and R values for each algorithm were averaged over the results of 100 learning processes.
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As shown in Figure 3A, the RFR algorithm exhibits the smallest RMSE value and the largest R value among
the six ML algorithms, indicating the best fitting effect. Therefore, the RFR algorithm was chosen to
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construct the Model-III for predicting V . Similarly, for the Model-IV model, the average RMSE and R
MX
values of six ML regression algorithms are summarized in Figure 3B. It is clear that compared to the other
four algorithms, the SVR and GBR algorithms exhibit better predictive ability because of their smaller
RMSE and larger R . Further analysis reveals that although the average RMSE value of the SVR algorithm is
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higher than that of the GBR algorithm, its standard deviation value is smaller. Moreover, the SVR algorithm
exhibits a higher R value and a smaller standard deviation value compared to the GBR algorithm. From the
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perspective of standard deviation value, a smaller value indicates greater model stability. From the above
analyses, the SVR algorithm was selected to build Model-IV for predicting V M23C6 . Figure 3C presents the
comparison of V values predicted by Model-III and calculated by the CLAPHAD method. The majority
MX
of data points are located near the diagonal (marked by the red dotted line in Figure 3C), with R values of
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> 0.9 for both training and testing sets. An R value of > 0.8 indicates a strong correlation, with the predicted
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[44]
values closely matching the observed values . This clearly shows that Model-III constructed by the RFR
algorithm has high predictive ability for V . Figure 3D plots the V M23C6 values predicted by Model-IV
MX
against those calculated by the CALPHAD method. Model-IV demonstrates strong predictive performance
in both the training and testing sets with an R > 0.9, comparable to the performance of Model-III. A good
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agreement between the predicted and the calculated results is also illustrated by the scatter points
distributed closely to the red diagonal. The above analysis results support a reasonable conclusion that the
prediction models constructed for the four crucial microstructural attributes of RAFM steels exhibit good
accuracy and reliability. These four sub-models (i.e., Model-I, Model-II, Model-III, and Model-IV) are
integrated together to form a microstructural model used for designing novel RAFM steels.

Design of novel RAFM steels
To achieve the design of RAFM steels with targeted microstructures and tensile properties, the forward and
reverse models as well as the microstructural model were coupled together to construct an integrated design
model, as shown in Figure 1. In this section, the effectiveness of the integrated design model is
demonstrated by designing novel RAFM steels satisfying specific structure and performance requirements.
It is crucial to avoid δ-ferrite, Laves, and Z-phase in RAFM steels as they are harmful for high-temperature
mechanical properties. MX precipitates exhibit excellent thermal stability, whereas M C precipitates are
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prone to coarsening at high temperatures. Consequently, enhancing the strength and creep resistance may
be achieved by increasing V while reducing V M23C6 . In this study, the targeted V and V M23C6 are set higher
MX
MX
[21]
and lower than the typical levels of < 0.2% and ~2%, respectively, found in conventional RAFM steels . The
newly designed RAFM steels are expected to exhibit a higher UTS value at 600 °C compared to conventional
RAFM steels, while maintaining a similar TE. The specific requirements are summarized as follows:
i. without δ-ferrite at NT;
ii. without Laves and Z-phase at TT;
iii. V ≥ 0.4% at TT;
MX
iv. V M23C6 ≤ 1.5% at TT;
v. test temperature (T ) = 600 °C, UTS ≥ 400 MPa, TE ≥ 20%.
test

Considering the particularity of this study, the performance requirements do not need to have a deviation of
[32]
< 10% between the predicted and targeted tensile properties, as was the case in our former work . One of
[32]
the biggest differences between this study and our previous work is the addition of structure