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Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 9 of 45

Figure 4. (A) Schematic diagram of machine learning-based approach to design new HEAs. This figure is quoted with permission
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from Yang et al. , copyright 2022, Elsevier; (B) schematic illustration of artificial neural network method, adapted from Risal
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et al. , copyright 2021, Elsevier; (C) actual versus predicted misfit and yield strength for 10-fold cross-validation of machine
learning models, insets show the error distribution around the mean. This figure is quoted with permission from Vazquez [90] ,
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copyright 2022, Elsevier; (D) elemental content distribution of predicted eutectic HEAs, adapted from Wu et al. , copyright
2020, Elsevier. HEA: High-entropy alloy.
of NN1 is surprising, given that it only used the elemental composition as input, while NN2 included
features related to thermodynamic properties.

Another work that shows consistent results with NN2 is that of Risal et al., where 598 alloy compositions
extracted from the literature were used as the training set, and the input parameters included the VEC,
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melting temperature of the alloy, enthalpy of fusion and variance of atomic radius . The basic structure of
the neural network used in their work is illustrated in Figure 4B. Interestingly, they achieved a prediction
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accuracy of 90.66%, slightly lower than that of NN1 and almost the same as NN2 in Nassar et al.’s work .
This result can be rationalized by the fact that NN typically only elucidates the correlation between
parameters and thus may not always reveal the underlying physical connection between the input and
output variables. Many examples exist in the literature on NNs, providing valuable predictions for HEAs’
microstructure type and material properties. However, further study is needed to understand the
mechanisms that lead to these valuable properties.

A common criticism of ML models is that they often lack interpretability despite their high predictive
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accuracy . Sure-independence screening and sparsifying operator (SISSO) is an example of an ML
method that can produce easy-to-understand relationships between the input and output variables. SISSO
can output these relationships as analytical equations such that the dependence of the output variables on
each input variable can be easily understood. Vazquez et al. recently used SISSO to predict the mechanical
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properties of alloys within a Ta-W-Nb-Mo-V refractory HEA (RHEA) system . This method functions
very differently from other ML algorithms as most methods attempt to filter the possible valuable features to