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Page 8 of 45 Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41

information and can thus be disregarded. Using this method, Liu et al. built a model that explored a 4500-
point compositional space in which seven compositions were identified that exhibit 230 < < 260 and the
lowest ΔT values. These results illustrate ML models’ capabilities to selectively tune a material system’s
properties using robust training datasets from previous studies and carefully selected input variables.

Most ML techniques are black-box ML with limited interpretability, which can hinder the development of
chemical insight into the origin of preferable properties. Recently, a new method to implement ML
described as a ML-based alloy design system (MADS) has been developed to predict alloys and maximize
[79]
the hardness within an Al-Co-Cr-Cu-Fe-Ni-V alloy system . This method is schematically illustrated in
Figure 4A and consists of four steps. First, a database containing alloy compositions within the selected
system and their measured hardness is established. Then a set of 142 features to model the hardness is
established and refined to remove all except the five most crucial factors. This refinement step is important
to reduce the computational cost and redundancy of information within the ML model. A model utilizing
the most critical parameters is constructed and then executed to optimize the composition toward
maximum hardness. Finally, the designed alloy compositions are experimentally fabricated and tested to
verify the predicted properties. The five features selected were the average deviation of the atomic weight,
the average deviation of the period column in the periodic table, the average deviation of the specific
volume, the valance electron concentration, and the mean melting point for the alloy. After exploring the
presented alloy system, the optimized composition was determined to be Co Cr Fe Ni V which was
18 7 35 5 35
predicted to have a hardness of 1,002 HV and was experimentally verified to show a hardness of 1,148 HV,
showing the prediction is in good agreement with the experimental value. This new HEA exhibits about
25% greater hardness than the maximum hardness in the original training dataset. The hardness
improvement illustrates ML methods’ ability to take previous experimental data and extrapolate it to
discover new compositions with better properties than previously achieved.

Artificial neural networks (ANNs) are common ML methods that use a layered architecture of input,
hidden, and output nodes trained to predict useful material properties such as phase formation, hardness,
and yield strength. The input layer consists of multiple nodes which hold values of the parameters that are
st
known either a priori or from databases. Then each node in the 1 hidden layer is calculated by a weighted
sum of the nodes from the input layer. Nodes in subsequent hidden layers are calculated by a weighted sum
of the nodes from the previous layer. Finally, the output layer consists of the target/output parameters
calculated from a weighted sum of the nodes from the hidden layer immediately preceding the output layer.
These parameters can include the predicted properties of the studied alloys, such as the hardness of a
material, the elastic properties, phase prediction classifier etc. The weights for every calculated sum are
initialized as a best guess and then adjusted to minimize the error between the predicted and experimental
values for training data. Once the error is minimized, the adjusted weights can then be used in conjunction
with input data for new alloy systems outside of the training set to predict properties of interest [81,84,85] .

Notably, Nassar et al. used two different ANNs (NN1 and NN2) to predict the phase formation with 37
[86]
possible elements in the alloy composition . NN1 had only composition data as its inputs and, thus, only
37 input nodes. NN2 used composition data and some calculated thermodynamic properties of each
composition, such as the entropy of mixing, enthalpy of mixing, valence electron concentration (VEC),
atomic radius difference, and Pauling electronegativity difference. The output node values were a binary of
0 or 1, where 1 indicates the formation of a single-phase solid solution (SS) or a solid solution plus
intermetallic (SS + IM). At the same time, 0 predicts a primary IM phase or IM + amorphous phase
structure. After training, the neural networks could accurately predict the type of microstructure given an
arbitrary composition with 92% and 90% accuracy for NN1 and NN2, respectively. The improved accuracy